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# Create 3x3 Matrix In Java

Create a button that will remove a random image-tile 8. Create a magic square of size ‘n*n’. How heavy are the three men individually? 3. This code checks that the input matrix is a pure rotation matrix and does not contain any scaling factor or reflection for example /** *This checks that the input is a pure rotation matrix 'm'. Next, we are going to add those two matrices using For Loop. Write a NumPy program to create a 3x3 identity matrix, i. If condition is true then. View Mudassir Kidwai’s profile on LinkedIn, the world's largest professional community. Additionally, I want to get to know how good these solutions are. The matrix command takes the entries of a matrix, optionally preceded by a ring and the dimensions of the matrix, and returns a matrix. Code in Java to calculate the determinant of a 3x3 matrix. Affine Transformations. When you run the program, the output will be: In the above program, the two matrices are stored in 2d array, namely firstMatrix and secondMatrix. When we construct a matrix directly with data elements, the matrix content is filled along the column orientation by default. () * functions (e. It is an online tool programmed to calculate the determinant value of the given matrix input elements. Atom TechSoft Outlook OST to PST Converter Software. Covariance Matrix • Representing Covariance between dimensions as a matrix e. They are, Matrix Determinant Matrix singular or not Adjoint matrix Matrix Inversion AA-1 = I (A-1)-1 = A Matrix Determinant - algorithm matrix A - a matrix size of 3x3. Accessing matrix elements. how to create a 3x3 matrix written in c++: #include #include<. Various "gets" and "sets" provide access to submatrices and matrix elements. Here is the code for inverse of a matrix and sample output data. See the following output. 5 Numerical Solutions to Differential Equations. Use of nested loops is recommended while printing 2d array in matrix form in java. GL_MODELVIEW matrix combines the view matrix and model matrix, but we keep them separately and pass the product of these 2 matrices to OpenGL's GL_MODELVIEW when it is required. Write a program to print the diagonal elements of. Affine Transformations. Hi how to print the diagonal elements of a two dimensional array using for loop Can any one help mePlzzzzzzzz. First of all, you only need to consider the left-top k*k matrix to find the k-th largest element. * Matrix does not have a constructor, so it must be explicitly initialized * using either reset() - to construct an identity matrix, or one of the set. An array is an object and what appears to be a 2D array is in fact an array of arrays. Pivot on matrix elements in positions 1-1, 2-2, 3-3, continuing through n-n in that order, with the goal of creating a copy of the identity matrix I n in the left portion of the augmented matrix. In this tutorial I will explain how to setup development environment for using OpenCV Java with Eclipse in Windows, so you can enjoy the benefits of garbage collected, very refactorable (rename variable, extract method and whatnot) modern language that enables you to write code with less effort and make less mistakes. To create a transformation matrix that performs two transformations at once, multiply the two source matrices,. The following code shows how to use the JTable class to create a simple table as part of a GUI. Today we shall learn about the multiplication of two matrices. It is possible to create a n x m matrix by listing a set of elements (let say n) and then making each of the elements linked to another 1D list of m elements. If we create a variable of integer type then, the array of int can only store the int values. You can set the range of minimum and maximum allowed random values. Java Program to add two matrices. Code a matrix by listing a series numbers separated by spaces or commas per row within the command window. Since we have not provided any. Like and share. Let's see a simple example to transpose a matrix of 3 rows and 3 columns. Matrix Multiplication In Java Using Methods. Get the free "Matrix Equation Solver 3x3" widget for your website, blog, Wordpress, Blogger, or iGoogle. A Toeplitz (or diagonal-constant) matrix is a matrix in which each descending diagonal from left to right is constant, i. When we construct a matrix directly with data elements, the matrix content is filled along the column orientation by default. The most important advantage of matrices is that the provide. Expanding Grid. The ' is a transpose operator, which flips matrices symmetrically around their diagonal axis. Alternatively, the matrix can be cast to a 3×3 matrix. [Assuming the 2D Array to be a square matrix with odd dimension i. This may not seem intuitive or exciting. The remaining part of the program is completely the Matrix multiplication of logic, and you can understand it, if you concentrate on the logic. to create a transformation matrix that applies the transformation s1 followed by s2, call rsMatrixLoadMultiply(&combined, &s2, &s1). Matching recipes (any size from 1x1 to 3x3 matrix) [solved] them to restrict some recipes, I know how to create new ones. Program to check matrix is symmetric or not in java // This program will find weather the matrix is symmetric or not. Use comma "," as separator and press "Plot Graph". If in the entered orders, the column of first matrix is equal to the row of second matrix, the multiplication is possible; otherwise, new values should be entered in the program. Aug 18, bcg matrix 2x3 by some brackets, 2008 matrix 2x3 by 3x3 homework help - cd, with. Because the matrix multiplication is associative. in the last line of the previous example. com,free GTU book download ,free IDP project,final year project for all branch download ,MCA. A matrix is a table of. Eigenvalues and Eigenvectors Projections have D 0 and 1. First you need to create a Matrix object: Matrix inputMatrix = new Matrix(data); data is a two dimensional array that holds the real data of your matrix. diag(INDArray in). I tried to do it with these numbers: 22 10 15 12 5 8 22 3 8 But when I run the program the matrix is: 22 10 15 12 5 88 22 3 8. So, a matrix of 2 X 2 was displayed, having its main diagonal with value 1 with return type as a float. Create ONE 2-D Rectangle array a. This number can determine whether a set of linear equations are solvable, in other words whether the matrix can be inverted. A 3-Dimensional vector can be represented by a "1-dimensional" array of size 3. To create an array list in Java, you declare an ArrayList variable and call the ArrayList constructor to instantiate an ArrayList object and assign it to the variable: ArrayList friends = new ArrayList(); You can optionally specific a capacity in the ArrayList constructor: ArrayList friends = new ArrayList(100); Note that the capacity is not a […]. Example 1: Find the inverse of $A = \left[ {\begin{array}{*{20}{c}} 1&2&3\\ 2&5&3\\ 1&0&8 \end{array}} \right]$ Solution: Step 1: Adjoin the identity matrix to the right side of A:. Create a button that will remove a random image-tile 8. [Assuming the 2D Array to be a square matrix with odd dimension i. Display the tiles in the right order for the correct image 7. The matrix objects are a subclass of the numpy arrays (ndarray). JAVA program to find the sum of diagonal elements of a square matrix This JAVA program is to find the sum of diagonal elements of a square matrix. Plaintext. Thank you Ronnie ! Topic archived. (String [] args) {int N = 5; // create a symmetric positive definite matrix Matrix A = Matrix. You take your input vector A: A = [a x a y a z]. This has the same effect as loading each element and converting it to a F32_4(RenderScript), multiplying the result by the 4x4 color matrix as performed by rsMatrixMultiply() and writing it to the output after conversion back to U8_4(RenderScript). For example, for a 2 x 2 matrix, the sum of diagonal elements of the matrix {1,2,3,4} will be equal to 5. The output matrix has the form of. The constructor should initialize the empty board to all zeros. I would like to have a plot with different background Color (please see link). Each matrix has fixed number of rows and columns and for multiplication to be feasible, the number of rows of first matrix must be equal to number of columns of second matrix. Write a program to perform 3X3 matrix addition. In this tutorial I will explain how to setup development environment for using OpenCV Java with Eclipse in Windows, so you can enjoy the benefits of garbage collected, very refactorable (rename variable, extract method and whatnot) modern language that enables you to write code with less effort and make less mistakes. Then using these two matrices you can do the multiplication. In this discussion, the method will be the static main method. Multi-dimensional arrays are built from multiple one-dimensional arrays. Eigenvalues code in Java Eigenvalues. Code a matrix by listing a series numbers separated by spaces or commas per row within the command window. Jython is an implementation of the Python programming language designed to run on the Java platform. The AbstractTableModel class is used as a data manager for the JTable. How To Write Nxn Matrix In Latex. For those who are confused by the Python 2: First input asks for the matrix size (n). Now we’ve known about LPS, FPS and kernel. Yaw, pitch, and roll rotations. Today we shall learn about the multiplication of two matrices. For matrix multiplication to take place, the number of columns of first matrix must be equal to the number of rows of second matrix. Creating Multiplication Table in Java A multiplication table is a table of numbers which lists product of a decimal sequence of numbers. To add two matrices in Java Programming, you have to ask to the user to enter the elements of both the matrix, now start adding the two matrix to form a new matrix. Use comma "," as separator. Multiplication of two matrices is little complicated as compared to the addition of the two matrices. to create a transformation matrix that applies the transformation s1 followed by s2, call rsMatrixLoadMultiply(&combined, &s2, &s1). Arrays are one of the most frequently used data structures in Java, therefore it’s crucial to understand how they work. numRows by A. How to create a method that takes in an array and sets all the borders to 1 It will end up looking like this: 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1. Write a NumPy program to create a 3x3 identity matrix. Scanner; class MainClass { int matrix [] []; int row, column; void create() { Scanner in = new Scanner (System. You may receive emails, depending on your notification preferences. There are more efficient algorithms available. print ("Enter number of rows in matrix : "); //rows and columns in matrix1 and matrix2 must be same for. A matrix is also known as array of arrays. You define (create or instance) the matrix this way: double a[3][3]; In this case, C defines a as a matrix possessing 9 double values. Consider a 3 X 3 matrix, s , of integers in the inclusive range [1, 9]. Unlike general multiplication, matrix multiplication is not commutative. Start with a simple bubble chart. We employ the latter, here. For such a small matrix, it seems ridiculous to need generalized SVD algorithms from libraries like LAPACK. Object: clone() Clone a matrix. This one would show you how to create a copy a matrix and how to compare two matrix to check if they are equal. Then call the inverse method:. A matrix resembles a table with rows and columns. Atom TechSoft Outlook OST to PST Converter Software. Let c be the result of the multiplication. That looks very complicated. Consider a 2D matrix of numbers from 0 to 9 with variable width and height. C Program for Matrix Multiplication Below is a program on Matrix Multiplication. Method 3 (Prints in matrix style Using Arrays. [2016-04-04] Challenge #261 [Easy] verifying 3x3 magic squares Description A 3x3 magic square is a 3x3 grid of the numbers 1-9 such that each row, column, and major diagonal adds up to 15. You are now following this blog post. Below is the syntax highlighted version of Matrix. Here is a code snippet for this: n = 3 m = 3 val = [0] * n for x in range (n): val[x] = [0] * m print(val) Program output will be:. It is suitable for use in any kind of Java applications or Web applications which need advanced MathML / Equation document authoring or document creation. The unit matrix is every nx n square matrix made up of all zeros except for the elements of the main diagonal that are all ones. 3x3, 5x5, 7x7 etc] Example, if the array contents is 3 5 4 7 6 9 2 1 8 Output through the method should be :. You can also use a method where values of matrix. See the following code. In the matrix multiplication Java program, initially user is prompted to enter the matrices. Angle + Axis - rotation angle (in Radians) around an axis. For matrix multiplication to take place, the number of columns of first matrix must be equal to the number of rows of second matrix. Below example shows how to take matrix data from the user inputs and display them. The example below demonstrates how to use a fixed sized matrix and convert to other matrix types in EJML. Write a program to print the diagonal elements of 3X3 matrix. A matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns that is treated in certain prescribed ways. Create a matrix. There is lot of usefull methods like resize, insert , remove, sort and lot of other methods. HAPPY CODING. Enter adjacency matrix. You can create an instance for an enum (just like creating an instance of a class) and assign a value into it. See the following code. (a) Check that A3 = 0 where 0 is a 3 3 matrix with every entry equal to 0. Method 3 (Prints in matrix style Using Arrays. One other method that can occasionally be useful is Nd4j. Create a 6 6 matrix matE with every. opts file in the startup directory and overriding the default memory settings (see this documentation for more information). (which represents the 3 rows of the matrix, the three elements present in each row of the matrix). Diagonalizing a 3x3 matrix. When you run the program, the output will be: In the above program, the two matrices are stored in 2d array, namely firstMatrix and secondMatrix. Like and share. First you need to create a Matrix object: Matrix inputMatrix = new Matrix(data); data is a two dimensional array that holds the real data of your matrix. Java is a general-purpose, mid-level, backend programming language with which you can build websites, web applications, Android applications for mobile and tablet, and other different kinds of software. For each edge (u, v), where u is white, run depth-first search for u recursively. to create a transformation matrix that applies the transformation s1 followed by s2, call rsMatrixLoadMultiply(&combined, &s2, &s1). In this post we will try to print an array or matrix of numbers at console in same manner as we generally write on paper. This is done by multiplying the vertex with the matrix : Matrix x Vertex (in this order. In Java, we create two-dimensional arrays (rows/columns) to hold our data. Two matrices with a given order can be multiplied only when number of columns of first matrix is equal to the number of rows of the second matrix. GridLayout; import javax. This is similar to above. The confusion matrix shows the ways in which your classification model. If condition is true then. • Examples: • Lab book of multiple readings over several days • Periodic table. The inner for loop iterates for the value of j = 0 to j < col. First find the determinant of matrix. Remember that to ﬁnd the transpose, the rows and columns are interchanged, so that adj(A) = CT =. Download the source and binary: matrix. Display the tiles in the right order for the correct image 7. Euler Angles – a 3D float vector representing the angle of rotation around each axis ( pitch/yaw/roll ). Now that we understand what 2D Arrays look like, and how to create them, we can focus on utilization. A matrix is a table of. The constructor should initialize the empty board to all zeros. (b) Replace the third column of A by the sum of the second and third columns. Example 3 The reﬂection matrix R D 01 10 has eigenvalues1 and 1. import java. In this tutorial, you’ll learn how to implement matrix multiplication in Python. For a square matrix, i. First you need to create a Matrix object: Matrix inputMatrix = new Matrix(data); data is a two dimensional array that holds the real data of your matrix. for 3 dimensions: cov(x,x) cov(x,y) cov(x,z) C = cov(y,x) cov(y,y) cov(y,z) cov(z,x) cov(z,y) cov(z,z) • Diagonal is the variances of x, y and z • cov(x,y) = cov(y,x) hence matrix is symmetrical about the diagonal. Each of these for-loops have 3 iterations. Rotation matrices are orthogonal as explained here. (matrix * vector) , as provided by rsMatrixMultiply (). Today we shall learn about the multiplication of two matrices. Alternatively, this can also be done by creating a java. Using 2D array to implement the matrices in java. MAGENTO TNT SHIPPING MATRIX MINDSTRETCH. It's guaranteed to be in that smaller matrix. In this tutorial I will explain how to setup development environment for using OpenCV Java with Eclipse in Windows, so you can enjoy the benefits of garbage collected, very refactorable (rename variable, extract method and whatnot) modern language that enables you to write code with less effort and make less mistakes. randint() function, we specify the range of numbers that we want that the random integers can be selected from and how many integers we want. 3 numbers in line. A declaration merely tells C what an object is. The constructor should initialize the empty board to all zeros. 2) You need to use an enclosing block if you want to include the printf() in the inner loop. Note that the correlation matrix is for a centered beam (on axis). Inverse Of 2x2 Matrix. You still seem to be thinking in terms of 2D arrays, but there ain't no such thing in Java®. Big list of c program examples. Inside the inner for loop, the program asks the user to enter the values in the matrix. Element at (0, 0) in the first matrix added with (0, 0) of the second matrix becomes the element at index (0, 0) in the resultant matrix too. Let's see another example where we are displaying transpose of a matrix. Aug 18, bcg matrix 2x3 by some brackets, 2008 matrix 2x3 by 3x3 homework help - cd, with. Ask Question. To create a transformation matrix that performs two transformations at once, multiply the two source matrices, with the first transformation as the right argument. Create ONE 2-D Rectangle array a. The inner for loop iterates for the value of j = 0 to j < col. Here, we are not creating another matrix. A few friends and I are creating a simulation based game using java where our "players" go out on an 11x11 matrix full of a Class called Chunk. Video Player is loading. how to create a 3x3 matrix written in c++: #include #include<. External Resources:. We can find inverse of a matrix in following way. • Often data come naturally in the form of a table, e. There is a difference between a definition and a declaration that you need to keep in mind. Since we have not provided any. For example, Sharpen: -1 -1 -1 -1 9 -1 -1 -1 -1 Blur: 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 Following is an example that performs a convolution using a 2D array (see Chapter 13, p. First find the determinant of matrix. import java. randint() function. Then call the inverse method:. diag(INDArray in). Euler Angles – a 3D float vector representing the angle of rotation around each axis ( pitch/yaw/roll ). PrintWriter; /** * The Matrix class holds a 3x3 matrix for transforming coordinates. Example 3 The reﬂection matrix R D 01 10 has eigenvalues1 and 1. Big list of c program examples. 5 Numerical Solutions to Differential Equations. Replace all 0 to random number from 10 to 20. Various constructors create Matrices from two dimensional arrays of double precision floating point numbers. You can optionally pass an existing matrix in result to avoid allocating a new matrix. Two matrices with a given order can be multiplied only when number of columns of first matrix is equal to the number of rows of the second matrix. Pivot on matrix elements in positions 1-1, 2-2, 3-3, continuing through n-n in that order, with the goal of creating a copy of the identity matrix I n in the left portion of the augmented matrix. PLAYING and GameState. Also read - matrix multiplication in java. Matrix Multiplication In Java – Using For Loop 1) Condition for multiplication of two matrices is -1st matrix column number equal to 2nd matrix row number. In order for the players to be able to interact with. From the resulting matrix, I retrieve new point coordinates from the third column ([1][3], [2][3], [3][3] if you will). It can't store other than int data type. (Note that the values in the convolution matrix add up to 1). NOTE: No unit conversion is done, the correlation matrix has the same unit system as the Twiss parameters. java $java MatrixCalculator Screen Shot. Previte Department of Mathematics Penn State Erie, The Behrend College Station Road Erie, PA 16563 (814)-898-6091 E-Mail [email protected] We can multiply two matrices in java using binary * operator and executing another loop. But, it is quite useful for graphics operations because it allows us to combine translation, scale and rotation transformations, simply by using matrix multiplication. Consider the below example, mat = [[10, 20, 30], [40, 50, 60], [70, 80, 80]] It can be considered a 3x3 matrix, there are 3 rows and 3 columns in 'mat' matrix. The constructor should initialize the empty board to all zeros. As each pixel is processed, a new image emerges based upon the calculated values. You may receive emails, depending on your notification preferences. The TicTacToe class contains a 3x3 two-dimensional array of integers. Next: Write a program in C for addition of two Matrices of same size. Create a 6 6 matrix matE with every. But, it is quite useful for graphics operations because it allows us to combine translation, scale and rotation transformations, simply by using matrix multiplication. For implementing matrix multiplication you’ll be using numpy library. Create NxN Matrix in Python/Numpy. In case of matrix multiplication, one row element of first matrix is multiplied by all columns of second matrix. You just will write the matrix in your code and the program will change as depend to size and calculate automatically as the matrix. The most important advantage of matrices is that the provide. Let's say you have a 3x3 matrix. ? MultiDimensional Array to/from file? Reading from a file to map a 2-dimensional array; Write unsigned char array to a file; RE: reading. Re: help to calculate eigenvalues of n*n matrix in java Posted 12 May 2011 - 08:18 PM I used recursion to find the determinant of a matrix. To create an array of random integers in Python with numpy, we use the random. Print In Assembly 8086. They define the vertices of a spherical triangle. Generate Barcode Reporting Services - creating barcodes in SSRS reports with data from database. Let's see a simple example to transpose a matrix of 3 rows and 3 columns. This calculator is designed to calculate$2\times 2$,$3\times3$and$4\times 4$matrix determinant value. Let's say we have a 3x3 grid, named gameBoard , with the value of our Tic-Tac-Toe game. Use comma "," as separator. regards, Ronnie van Aarle. You can create the matrix using integer numbers or decimal numbers, and control the number of decimal number precision. eye(A) Create an identity matrix which is A. A matrix is also known as array of arrays. Two matrices with a given order can be multiplied only when number of columns of first matrix is equal to the number of rows of the second matrix. Normalization can be applied by setting normalize=True. to create a transformation matrix that applies the transformation s1 followed by s2, call rsMatrixLoadMultiply(&combined, &s2, &s1). In this program, you'll learn to add two matrices using multi-dimensional arrays in Java. Write a C program to read elements in a matrix and find the sum of elements of each row and columns of matrix. It is possible for arrays to have multiple dimensions. Import the array from numpy inside matrix. Note that the correlation matrix is for a centered beam (on axis). This code checks that the input matrix is a pure rotation matrix and does not contain any scaling factor or reflection for example /** *This checks that the input is a pure rotation matrix 'm'. The idea is to represent your points as 3x1 vectors, and transformation is then simply multiplication by 3x3 matrix. If one of the pivoting elements is zero, then first interchange it's row with a lower row. To find number of columns in i-th row, we use mat [i]. For implementing matrix multiplication you’ll be using numpy library. diagonal elements are 1, the rest are 0. For such a small matrix, it seems ridiculous to need generalized SVD algorithms from libraries like LAPACK. Matrix should be square. WebAssign Student Help; COVID-19 Impacts on Your Courses; What's New in WebAssign. This article describes one of the ways to find the adjacent elements for a particular element in a given square Matrix. An array is the collection of same data type values. The TicTacToe class contains a 3x3 two-dimensional array of integers. MULTIPROD is a powerful, quick and memory efficient generalization for N-D arrays of the MATLAB matrix multiplication operator (*). Java-Read Text Files And Store Them As Arrays; Read DATA From A text file and save it in database and print the logs by using JAVA. Matrix Multiplication In Java Using Methods. The core and starting structure for any project is most likely matrix_t: var my_matrix = new jsfeat. In this core java programming tutorial will learn how to add two matrices in java. For such a small matrix, it seems ridiculous to need generalized SVD algorithms from libraries like LAPACK. Below I have shared program to find inverse of 2×2 and 3×3 matrix. Display the tiles in the right order for the correct image 7. You just will write the matrix in your code and the program will change as depend to size and calculate automatically as the matrix. Create ONE 2-D Rectangle array a. The inverse method is a static method and it can be called for any matrix of type Matrix. Introduction. Write a program to enter an integer number ‘n’. Create a magic square of size ‘n*n’. for Java and C++ code to implement these rotations click here. zip (Updated: 2020-03-26) This example shows how to integrate Matrix4 class with OpenGL. In order for the players to be able to interact with. A matrix is also known as array of arrays. Affine Transformations. If a smaller matrix is constructed from a larger matrix, the top, left submatrix of the larger matrix is chosen, e. No new replies allowed. It is possible for arrays to have multiple dimensions. You can create a kernel with left side is positive weights and right side is negative weights to make a new effect. In order for the players to be able to interact with. This is done by multiplying the vertex with the matrix : Matrix x Vertex (in this order. To reach cell m,n only permissible cells are the cells on left, up and diagonally up. PROGRAM: [code]#include int main() { int a[3][3],b[3][3],c[3][3],i,j,k,sum; printf(" Enter the matrix elements of A. The necessary condition: R2(Number of Rows of the Second Matrix) = C1(Number of Columns of the First Matrix). Matrix Construction. The matrix objects are a subclass of the numpy arrays (ndarray). After downloading, the following should work in any JDK 1. It's guaranteed to be in that smaller matrix. , spreadsheet, which need a two-dimensional array. Inverse of 3$\times$3 matrices. I’ve created a camera class with 4 vectors (right, up, forward and origin) and a moveForward method (in java’s OpenGL binding LWJGL) which moves the character forward with a simple origin + forward vector addition, but now I’m on a rotation around the Y axis to simulate turning left/right. Create a java program that has three version. Consider the code for passing some 3x3 prebuilt pointer array. Code in Java to calculate the determinant of a 3x3 matrix. product [r1] [c2] You can also multiply two matrices without functions. Program to find Deteminant of 2x2 Matrix Below is a program to find the determinant of a 2x2 matrix. if all elements of the current matrix in 3x3 aperture x 0 −1≤x≤x 0 +1, y 0 −1≤y≤y 0 +1 are inside the matrix (i. Below is the syntax highlighted version of Matrix. Various constructors create Matrices from two dimensional arrays of double precision floating point numbers. Matching recipes (any size from 1x1 to 3x3 matrix) [solved] them to restrict some recipes, I know how to create new ones. So, I wrote a simple & small Java method which does the job All you need to do is, put this method inside some class (better make it static) Pass the matrix along with its order and get the determinant output…. A few friends and I are creating a simulation based game using java where our "players" go out on an 11x11 matrix full of a Class called Chunk. The fourth variable you created, d, is built up out of the smaller components already defined, to create a 3x3 matrix as shown at right. An array is the collection of same data type values. Let's see another example where we are displaying transpose of a matrix. 451 546 456. Each element cij is ai1 x b1j + ai2 x b2j + … + ain x bnj. Now that we understand what 2D Arrays look like, and how to create them, we can focus on utilization. toString()) Arrays. filter_none. That looks very complicated. Download Add matrix program class file. JButton; import javax. A11 — First row, first column of matrix. Program to check matrix is symmetric or not in java // This program will find weather the matrix is symmetric or not. Matrix Lesson 2: Cramer’s rule Dave Coulson, 2013 2. Example 1: Find the inverse of$ A = \left[ {\begin{array}{*{20}{c}} 1&2&3\\ 2&5&3\\ 1&0&8 \end{array}} \right] \$ Solution: Step 1: Adjoin the identity matrix to the right side of A:. Code in Java to calculate the determinant of a 3x3 matrix. A matrix is diagonalizable if it is similar to a diagonal matrix. This is the key to the confusion matrix. In our example, i. In this discussion, the method will be the static main method. (a) Check that A3 = 0 where 0 is a 3 3 matrix with every entry equal to 0. We can multiply two matrices in java using binary * operator and executing another loop. Python 3x3 Matrix. An question asked by zoho corporation during interview was to write a program to read a matrix spirally. java from §9. Create a magic square of size ‘n*n’. See the output below. Multi-dimensional arrays are built from multiple one-dimensional arrays. EJML provides support for fixed sized matrices and vectors up to 6x6, at which point it loses its advantage. The Create 3x3 Matrix block creates a 3-by-3 matrix from nine input values where each input corresponds to an element of the matrix. MATLAB (Matrix Laboratory) adalah sebuah lingkungan komputasi numerikal dan bahasa pemrograman komputer generasi keempat. A few friends and I are creating a simulation based game using java where our "players" go out on an 11x11 matrix full of a Class called Chunk. * Matrix does not have a constructor, so it must be explicitly initialized * using either reset() - to construct an identity matrix, or one of the set. Let’s add 5 to all the values inside the numpy array. , spreadsheet, which need a two-dimensional array. Alternatively, the matrix can be cast to a 3×3 matrix. This has the same effect as loading each element and converting it to a F32_4(RenderScript), multiplying the result by the 4x4 color matrix as performed by rsMatrixMultiply() and writing it to the output after conversion back to U8_4(RenderScript). A 3x3 matrix implementation : Matrix « 2D Graphics GUI « Java. det(A) Determinant of the matrix inv(A) Inverse of a matrix pinv(A) Pseudo-inverse of a matrix rref(A) Reduced row echelon form of A trace(A) Trace of the. Andrew Mao • 2 years ago. to convert Celsius to Fahrenheit; Write a program to display grade message according. Each element cij is ai1 x b1j + ai2 x b2j + … + ain x bnj. Matrix: A matrix is a collection of data in rows and columns format. We can find inverse of a matrix in following way. numCols normF(A) Frobenius normal of the matrix. Below is the syntax highlighted version of Matrix. 5 Numerical Solutions to Differential Equations. Digi, Oct 13 I'm a newbie at Java :}. * * @param m The 3x3 matrix to set. java from §9. This array will store the information for the tiles (width, height, x-start, y-start) you are moving 6. A matrix is also known as array of arrays. Let’s check out some simple examples. in ); System. The entries of a matrix can be specified as a flat list of elements, a. 1,2,3,4,5,6,7,8,9,4,5 Thank you for your suggestions. Eigenvalues code in Java Eigenvalues. 4 OpenCV supports Java. /***** * Compilation: javac Matrix. random (N, N); A = A. JButton; import javax. [Assuming the 2D Array to be a square matrix with odd dimension i. A declaration merely tells C what an object is. Import the array from numpy inside matrix. I multiply the identity matrix with the rotation matrices (each separately). zip (Updated: 2020-03-26) This example shows how to integrate Matrix4 class with OpenGL. toString()) Arrays. def plot_confusion_matrix(cm, classes, normalize=False, title='Confusion matrix', cmap=plt. Permutations have all j jD1. They define the vertices of a spherical triangle. I would like to have a plot with different background Color (please see link). In this post we will try to print an array or matrix of numbers at console in same manner as we generally write on paper. Find more Mathematics widgets in Wolfram|Alpha. for example jump 3 numbers ant print the fourth. java Below is the syntax highlighted version of Eigenvalues. This may not seem intuitive or exciting. Create Numpy Array From Python Tuple. numCols normF(A) Frobenius normal of the matrix. A matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns that is treated in certain prescribed ways. You define (create or instance) the matrix this way: double a[3][3]; In this case, C defines a as a matrix possessing 9 double values. Applying a 3x3 Matrix Convolution: Matrix convolutions work by averaging pixel colors with those of surrounding pixels using this process. Create two objects of the class and each of which refers one 2D matrix. In this core java programming tutorial will learn how to add two matrices in java. An array is the collection of same data type values. 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To create an empty multidimensional array in NumPy (e. Consider costMatrix as the given matrix and a position m,n. Atom TechSoft Outlook OST to PST Converter Software. For example, in order to create a translate(x,y,z) method, you would implement a makeTranslation(tx,ty,tz) method, which makes use of a static helper method doMakeTranslation(tx,ty,tz, dst[][]),. 2 where the sum of any row, column or diagonal is always equal to same number. Source Code. Take the kernel demonstrated above: the mathematics of this matrix results in a value that is the average of all pixels in a 3x3 pixel grid. As each pixel is processed, a new image emerges based upon the calculated values. 1; 1/—its signs are reversed by R. To multiply matrix a by matrix b, the number of columns in a must be the same as the number of rows in b, and the two matrices must have elements of the same or compatible types. JFrame; public class GridTest extends JFrame { public static. This article describes one of the ways to find the adjacent elements for a particular element in a given square Matrix. reshape () method. In this post, we will answer this zoho interview question. Samsung's Galaxy Book lineup is now available to buy in the U. Image Transcriptionclose. Easily Convert EML to PST format by using EML to PST converter. Import the array from numpy inside matrix. 2x2 Matrix Multiplication Calculator is an online tool programmed to perform multiplication operation between the two matrices A and B. If a smaller matrix is constructed from a larger matrix, the top, left submatrix of the larger matrix is chosen, e. You can change the matrix dimension by entering the number of rows and columns. The 3x3 matrix that we derived above is called an Affine Transform. Another difference is that numpy matrices are strictly 2-dimensional, while numpy arrays can be of any dimension, i. To reference an item in an enum, use enumName. Yaw, pitch, and roll rotations. The complete source resides in the one file above. The convolution technique takes pixels from left to right and from top to bottom. Plaintext. isRotationMatrix. OnBarcode provides professional barcode software and libraries for you. I have a 3x3 identity matrix. A is the 3x3 matrix of x, y and z coefficients; X is x, y and z, and ; B is 6, −4 and 27; Then (as shown on the Inverse of a Matrix page) the solution is this: X = A-1 B. First, is the easiest. Let's see a simple example to transpose a matrix of 3 rows and 3 columns. Once you do that, the 3x3 matrix on the right half will be the inverse. Gauss Jordan Elimination Calculator (convert a matrix into Reduced Row Echelon Form). Consider the below example, mat = [[10, 20, 30], [40, 50, 60], [70, 80, 80]] It can be considered a 3x3 matrix, there are 3 rows and 3 columns in 'mat' matrix. Below is the syntax highlighted version of Matrix. */ package android. columns and rows is the same as defining width and height for image. The first step is to create a matrix using the keyword (since the keyword is shorter than 9 letters, just start the alphabet again until the matrix is full). In 2 nd function number of rows was 3, and the column was 3. com,free GTU book download ,free IDP project,final year project for all branch download ,MCA. Program to find Deteminant of 2x2 Matrix Below is a program to find the determinant of a 2x2 matrix. can be obtained by using the cofactor. Then do row operations until the left half becomes the identity matrix. You can create the matrix using integer numbers or decimal numbers, and control the number of decimal number precision. Enter elements in the first matrix: Enter elements in the second matrix: First matrix is: 0 0 0 0 0 0 0 0 0 Second matrix is: 0 0 0 0 0 0 0 0 0 Adding two matrices: 0 0 0 0 0 0 0 0 0 Samual Sam Published on 17-Sep-2018 15:55:48. You can also use a method where values of matrix.


text:
# tf.strided_slice

tf.strided_slice(
input_,
begin,
end,
strides=None,
var=None,
name=None
)

Defined in tensorflow/python/ops/array_ops.py.

See the guide: Tensor Transformations > Slicing and Joining

Extracts a strided slice of a tensor (generalized python array indexing).

Instead of calling this op directly most users will want to use the NumPy-style slicing syntax (e.g. tensor[..., 3:4:-1, tf.newaxis, 3]), which is supported via tf.Tensor.getitem and tf.Variable.getitem. The interface of this op is a low-level encoding of the slicing syntax.

Roughly speaking, this op extracts a slice of size (end-begin)/stride from the given input_ tensor. Starting at the location specified by begin the slice continues by adding stride to the index until all dimensions are not less than end. Note that a stride can be negative, which causes a reverse slice.

Given a Python slice input[spec0, spec1, ..., specn], this function will be called as follows.

begin, end, and strides will be vectors of length n. n in general is not equal to the rank of the input_ tensor.

In each mask field (begin_mask, end_mask, ellipsis_mask, new_axis_mask, shrink_axis_mask) the ith bit will correspond to the ith spec.

If the ith bit of begin_mask is set, begin[i] is ignored and the fullest possible range in that dimension is used instead. end_mask works analogously, except with the end range.

foo[5:,:,:3] on a 7x8x9 tensor is equivalent to foo[5:7,0:8,0:3]. foo[::-1] reverses a tensor with shape 8.

If the ith bit of ellipsis_mask is set, as many unspecified dimensions as needed will be inserted between other dimensions. Only one non-zero bit is allowed in ellipsis_mask.

For example foo[3:5,...,4:5] on a shape 10x3x3x10 tensor is equivalent to foo[3:5,:,:,4:5] and foo[3:5,...] is equivalent to foo[3:5,:,:,:].

If the ith bit of new_axis_mask is set, then begin, end, and stride are ignored and a new length 1 dimension is added at this point in the output tensor.

For example, foo[:4, tf.newaxis, :2] would produce a shape (4, 1, 2) tensor.

If the ith bit of shrink_axis_mask is set, it implies that the ith specification shrinks the dimensionality by 1. begin[i], end[i] and strides[i] must imply a slice of size 1 in the dimension. For example in Python one might do foo[:, 3, :] which would result in shrink_axis_mask equal to 2.

NOTE: begin and end are zero-indexed. strides entries must be non-zero.

t = tf.constant([[[1, 1, 1], [2, 2, 2]],
[[3, 3, 3], [4, 4, 4]],
[[5, 5, 5], [6, 6, 6]]])
tf.strided_slice(t, [1, 0, 0], [2, 1, 3], [1, 1, 1])  # [[[3, 3, 3]]]
tf.strided_slice(t, [1, 0, 0], [2, 2, 3], [1, 1, 1])  # [[[3, 3, 3],
#   [4, 4, 4]]]
tf.strided_slice(t, [1, -1, 0], [2, -3, 3], [1, -1, 1])  # [[[4, 4, 4],
#   [3, 3, 3]]]

#### Args:

• input_: A Tensor.
• begin: An int32 or int64 Tensor.
• end: An int32 or int64 Tensor.
• strides: An int32 or int64 Tensor.
• begin_mask: An int32 mask.
• end_mask: An int32 mask.
• ellipsis_mask: An int32 mask.
• new_axis_mask: An int32 mask.
• shrink_axis_mask: An int32 mask.
• var: The variable corresponding to input_ or None
• name: A name for the operation (optional).

#### Returns:

A Tensor the same type as input.

format: plain


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# Tag Info

## Hot answers tagged homomorphic-signatures

6

Look at group signatures (but use one of the more modern schemes; they are proven secure). The signature can be applied to a running counter, or a random challenge. Group signatures also give you a lot of "management" options which can be useful depending on the application. If you don't need them, then you can use ring signatures (but the verifier has to ...

3

Concerning your very broad question: Wikipedia can tell you about homomorphic signatures. However, its application is quite specific, and I have no idea if it fits your scenario/requirements. The homomorphic property has direct consequences for the signatures: It can not achieve existential unforgeability, because this contradicts the homomorphic property (...

2

There are some possible advantages to threshold signing. First, it enables a more flexible setting where the key can be divided into $n$ parts and any subset of $t$ can be used to sign. Second, you can go from holding a single key in one place to distributing it and back without making any changes. Third, you can achieve a type of proactive security by ...

2

There are two major families of signature schemes that bear some resemblance what you described. Code-based signatures: Courtois–Finiasz–Sendrier, or CFS The CFS family of signature schemes is based on code-based cryptography first introduced by Robert McEliece in 1978 and dualized by Niederreiter. We work with binary linear codes, of length $n$ and rank $... 2 First start with some notation. Say we have a plaintext space$P$which forms a group. And an encryption function which goes from the plaintext space to the ciphertext space, say$E : P\to C$.$E$is homomorphic if$E$forms a group homomorphism, i.e. given$E(x)$and$E(y)$for$x,y\in P$we can efficiently construct$E(x\cdot y)$without the private key, ... 1 Can Bob, without interacting with Alice, generate a new aggregate signature for the entire message set, i.e. (M,s′), that validates with Alice's public key? That would be troubling if Bob could sign anything verifiable by Alice's key (on behalf Alice). if there is a simpler and more efficient method available if there is only one signer. I am mainly ... 1 If I understand you correctly, you want that given$\mathit{pk}, \mathit{pk}'$, one can publicly decide whether or not$\mathit{sk} < \mathit{sk}'$(lexicographically) for the corresponding secret keys. Such a signature scheme would inherently be insecure. This is because given your public key$\mathit{pk}^*$, anyone would be able to run a binary ... 1 Let me try to rephrase your question in a way for which I might have an answer: Is there a way for Alice to give Bob a "limited signing key" (LSK) such that: Bob can freely generate up to$n\$ keys (or other messages) and sign them using the LSK issued by Alice; anyone can verify that these keys/messages were signed by an LSK that was issued by ...

1

Anybody can run any of the usual generators for asymmetric primitives as many times as they want. And they can do this without compromising the security of the private key. Generally the trust of a key pair by a user is however not in the private key, but in the public key or certificate around the public key. Now you could embed a signed token in the ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
## Article: Why Gaming is Good for Computers and AlphaGo is not AI by Itself

Title: 10 Breakthrough Technologies 2017: Reinforcement Learning Link: https://www.technologyreview.com/s/603501/10-breakthrough-technologies-2017-reinforcement-learning/ Source: surfin' Why has reinforcement learning recently become so formidable? The key is combining it with deep learning, a technique that involves using a very large simulated neural network to recognize patterns in data My Perspective on this: This is a good article not only for what …


text:
# Does there exist a functorial splitting for the weight filtration (of singular cohomology)?

There are plenty of examples of varieties whose singular cohomology with rational coefficients considered as a mixed Hodge structure does not decompose as the direct sum of its pure (weight) factors. Yet if we consider the cohomology just as filtered vector spaces over rationals, such a decomposition certainly exist (for any variety).

My question is: could there exist a functorial decomposition like this (say, for the singular cohomology as a functor from the category of all smooth complex varieties), or does there exist some obstruction for such a functorial splitting?

-

Mikhail,

This is an interesting question. But I think that the answer is no, there would be no functorial splitting of the weight filtration as filtered vector spaces.

This needs a bit of work perhaps, but here is my example. Let $E$ be an elliptic curve. Let the $\sigma$ the involution given by $-1$ in the group law. Choose a non $2$-torsion point $p$. Then $q=\sigma(p)\not= p$. By duality, we may work with homology. Choose small loop $\gamma_p$ about $p$ and let $\gamma_q$ be its image under $\sigma$. Note that the class $[\gamma_p+\gamma_q]=0$ in $H_1(E-\{p,q\})$. Then there is an exact sequence $$\mathbb{Q}^2\to H_1(E-\{p,q\})\to H_1(E)\to 0$$ where the first map sends $(a,b)$ to $a[\gamma_p]+b[\gamma_q]$. A splitting would send $H_1(E-\{p,q\})$ to $W_0=span(\gamma_p)$, or to the anti-invariant part of $\mathbb{Q}^2$ under $\sigma$. However, functoriallity should imply that the splitting ought to be invariant.

Added This example is a bit fishy as it stands (see comments) but I think the basic strategy should work. I'll try to fix it in the morning.

-
I am sorry; could you explain the second to last statement? This seems a bit strange: similar arguments should work for an elliptic curve over a finite field, yet in this case there exists a canonical splitting for the filtration. –  Mikhail Bondarko Nov 20 '10 at 23:00
OK, I see. I realize that I was probably hasty in the way I set up my example, since Hodge theoretic (and presumably Galois theoretic) extension class corresponding to $$0\to {\mathbb Q}(1)\to H_1(E-\{p,q\})\to H_1(E)\to 0$$ vanishes because p and q are linearly equivalent. Let me try again with E any curve with involution such that $E/\sigma$ has positive genus. Although I should probably work it out carefully. By the way, it may be more efficient to communicate by email. It would be nice to get this example sorted out. –  Donu Arapura Nov 20 '10 at 23:37
Dear Donu, I will certainly be very glad to get an e-mail from you, and will write you if I will have anything big on the subject. –  Mikhail Bondarko Nov 21 '10 at 0:19
An observation on elliptic curves over finite fields (that fails over infinite ones): all points are torsion all curves have complex multiplication. –  Mikhail Bondarko Nov 21 '10 at 0:24

There is the Deligne splitting. I take this from Peters and Steenbrink's book, Section 3.1.

For a complex variety $X$, we define $I^{p,q} \subseteq H^{\ast}(X, \mathbb{C})$ by $$I^{p,q} := F^p \cap W_{p+q} \cap \left( \overline{F}^q \cap W_{p+q} + \sum_{j \geq 2} \overline{F^{q-j+1}} \cap W_{p+q-j} \right).$$

Then $H^{\ast}(X, \mathbb{C}) = \bigoplus I^{p,q}$ and $W_k \otimes \mathbb{C} = \bigoplus_{p+q \leq k} I^{p,q}$ and $F^p = \bigoplus_{r \geq p} \bigoplus_s I^{r,s}$.

In particular, defining $U_k = \bigoplus_{p+q=k} I^{p,q}$ gives a splitting of the weight filtration tensored with $\mathbb{C}$. If I am not mistaken, it is functorial.

The Deligne splitting only exists with $\mathbb{C}$ coefficients. I think Donu Arapura's answer here is fairly convincing that there is no splitting with $\mathbb{Q}$ or $\mathbb{R}$ coefficients.


text:
Archives

The second order differential equation with nonlinear damping $u^{\prime\prime}(t)=u^{\prime}(t)^q(c_1+c_2u(t)^p)$
by MENG-RONG LI (李明融) and X. Z. LIN(林脩竹)
Vol. 32 No. 4 (2004)


text:
# Preventing a camera's roll from drifting

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I had actually thought I got my 6DOF camera working properly, but only recently I've noticed that whenever I rotate the yaw and pitch 'too much', the roll seems to drift apart and the three basis vectors are not orthogonal any more. So my guess is that I have to orthogonalise the matrix (which is generated using a FromYawPitchRoll() method) because I'm storing the rotations incrementally, however I'm unsure how to actually do this. I've looked around and the only thing I could find is the Gram-Schmidt algorithm. My math background being very weak, I couldn't really understand how the whole thing worked. Also, just to be sure, checking the dot products of all three vectors should return 0 if they are mutually perpendicular right? Since that's how I'm checking if the three vectors are orthogonal. Any help would be greatly appreciated. :)

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If you renormalize the matrix periodically this shouldn't happen, or be noticeable. But you could just reorthogonalize the matrix with cross products. This will be biased towards a particular axis of your choosing.

Ideally though wouldn't make incremental corrections on the output value, the matrix. You'd increment the source values, such as the angles like you mentioned, or a quaterion, and use that to regenerate the matrix.

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Quote:
 Ideally though wouldn't make incremental corrections on the output value, the matrix. You'd increment the source values, such as the angles like you mentioned, or a quaternion , and use that to regenerate the matrix.

The matrix used to get the camera's three basis vectors is actually converted from a quaternion which represents the total rotation. Every frame, a matrix is created using yaw pitch and roll values, converted to a quaternion which is multiplied by the total rotation. Sorry, I forgot to explain that.

For clarity, it goes like this:

Take the change of rotation in yaw, pitch and roll values
Build a matrix representing the change
Convert that matrix to a quaternion
Multiply the converted quaternion with the totalRotation quaternion

Whenever the RotateYawPitchRoll() is called and then:

Convert totalRotation to matrix
Orthoganalise the matrix here????
Retrieve the camera's three basis vectors from that matrix
Normalise those vectors

Whenever Update() is called, which is every frame.

[Edited by - -Datriot- on April 22, 2009 8:12:27 AM]

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Why do you create a matrix only to convert it to a quaternion? Why not just create the quaternion directly?

After calling CreateFromYawPitchRoll() a matrix should be returned which is completely orthogonal, there should be no reorthogonalization required after that. Though i dont know how you're using both quaternions and YawPitchRoll.. there's far too much conversion going on here.

it shouldbe:

Quat dQ = GetIncrementalRotation();
finalQ *= dQ;

finalMatrix = Matrix(finalQ);

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I'm not sure about other methods, but the way I orthonormalize matrices is this:

void OrthoNormalize(Matrix3& m){	m[0] /= m[0].Length();	m[1] /= m[1].Length();	m[2] = m[0].CrossProduct(m[1]);	m[2] /= m[2].Length();	m[0] = m[1].CrossProduct(m[2]);}

Assuming your 0 and 1 columns are more or less correct, you can automatically get the correct 2 column using the cross product. The final step ensures that 0 column is orthogonal to 1 column.

edit:
Added m[2] normalize, might be required.

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Quote:
 For clarity, it goes like this:Take the change of rotation in yaw, pitch and roll valuesBuild a matrix representing the changeConvert that matrix to a quaternionMultiply the converted quaternion with the totalRotation quaternionWhenever the RotateYawPitchRoll() is called and then:Convert totalRotation to matrixOrthoganalise the matrix here????Retrieve the camera's three basis vectors from that matrixNormalise those vectorsWhenever Update() is called, which is every frame.
Just to echo what bzroom said, it sounds like you're doing some unnecessary conversions and normalizations here. Here's a stripped-down version with the redundancies removed:
- Build a quaternion from the yaw, pitch, and roll delta values- Multiply the delta quaternion with the totalRotation quaternion- Normalize the totalRotation quaternion- Convert the totalRotation quaternion to matrix form if/as needed
Let me know if that requires any clarification.

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The roll of the camera still persists. I reduced the number of conversions by creating the deltaQuaternion directly from the yaw, pitch and roll angles instead of converting it from a matrix like you said, using the following member function.
        void FromYawPitchRoll(float yaw, float pitch, float roll)        {            yaw = DegreesToRadians(yaw);            pitch = DegreesToRadians(pitch);            roll = DegreesToRadians(roll);            Quaternion<T> y, p, r;            y = Quaternion<T>(0, sin(-yaw / 2), 0, cos(-yaw / 2));            p = Quaternion<T>(sin(-pitch / 2), 0, 0, cos(-pitch / 2));            r = Quaternion<T>(0, 0, sin(-roll / 2), cos(-roll / 2));            // Could the order of multiplication matter here???            *this = (y * p * r);            Normalise();        }

After that, I used Thrump's method of orthoganalising the three basis vectors, just in case, like so:
// Gets the vectors from the matrix created from totalRotationright = vector3f(mat(0, 0), mat(1, 0), mat(2, 0));up = vector3f(mat(0, 1), mat(1, 1), mat(2, 1));// Orthoganalises themright.Normalise();up.Normalise();forward = -vector3f::Cross(right, up);forward.Normalise();right = vector3f::Cross(up, forward);

Rotating the pitch of the camera keeps the dot products as (0, 0, 0), but any change the yaw or roll knocks it all off balance and the three vectorsaren't orthogonal anymore.

Could it be that the operations I'm doing is biased to a certain axis? Since changing the pitch doesn't 'break' the orthoganal vectors.

[Edited by - -Datriot- on April 22, 2009 9:33:05 AM]

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Quote:
 The roll of the camera still persists.
Can you clarify what you mean by 'the roll of the camera persists'? Earlier you mentioned that the orientation is drifting out of orthogonality, but 'the roll still persists' seems like it probably means something different.
Quote:
  void FromYawPitchRoll(float yaw, float pitch, float roll) { yaw = DegreesToRadians(yaw); pitch = DegreesToRadians(pitch); roll = DegreesToRadians(roll); Quaternion y, p, r; y = Quaternion(0, sin(-yaw / 2), 0, cos(-yaw / 2)); p = Quaternion(sin(-pitch / 2), 0, 0, cos(-pitch / 2)); r = Quaternion(0, 0, sin(-roll / 2), cos(-roll / 2)); // Could the order of multiplication matter here??? *this = (y * p * r); Normalise(); }
Couple of tips here. It would be a good idea to create a 'from axis-angle' function for creating your rotation functions. Doing it manually like this is laborious and highly error-prone. (This applies in general, as well, for any oft-repeated bit of code.)

Assuming the deltas are small, the order of multiplication does not matter (much) here. In any case, it's probably not the cause of the problem. Finally, there's no need to call Normalize() at the end of the function (the quaternion will already be sufficiently close to unit length).
Quote:
 After that, I used Thrump's method of orthoganalising the three basis vectors, just in case, like so:
This is completely unnecessary and out of place in the given context. The only 're-orthogonalization' you should need to do in the given context is to call Normalize() on your orientation quaternion at the end of each update. That's it - that will be sufficient to prevent any noticeable numerical error from accumulating.
Quote:
 Rotating the pitch of the camera keeps the dot products as (0, 0, 0), but any change the yaw or roll knocks it all off balance and the three vectorsaren't orthogonal anymore.
Are you actually seeing incorrect behavior in your simulation, or is you observation based only on the dot product values that you're seeing? If the latter, can you post an example of a set of values that looks incorrect to you (i.e. something other than zeros)?

Are the values small? Are they displayed in scientific notation? It may be that you're simply misinterpreting numerical error as non-orthogonality.

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Quote:
 Can you clarify what you mean by 'the roll of the camera persists'? Earlier you mentioned that the orientation is drifting out of orthogonality, but 'the roll still persists' seems like it probably means something different.

Sorry about that, I should have said 'the problem with the roll still persists'.

Quote:
 Are you actually seeing incorrect behavior in your simulation, or is you observation based only on the dot product values that you're seeing?

It is very noticable on the simulation itself, that's how I first become aware of the problem. I just printed the dot products to make sure that the problem was with the camera. The dot products printed off usually range from -10 to 10.

I'm sure I'm doing everything right, I'll check all the relevant functions to make sure there aren't any errors in the calculations.

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Quote:
 The dot products printed off usually range from -10 to 10.
Well, that's not right :)

If you're seeing values of that magnitude, then the problem is not drift or accumulated numerical error but rather an error in your code somewhere, in which case double-checking the various support functions for correctness is indeed a good idea.

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1. Jul 11, 2013

### Naveen3456

I was reading about Galileo's gravity and there I came across the formula.

F= -mg.

Galileo said that Force is proportional to mass but in the opposite direction. I don't want to discuss whether he was right or wrong.

I just want to ask that when he replaced the proportionality sign and used a 'constant' 'g', why did he use the multiplication sign (this is the standard practice till today).

In other words, whenever there is an interaction why only multiplication sign is used and not the plus (+)sign.

Plus sign can also mean some kind of 'interaction'.

Doesn't F= - (m+g) show some kind of interaction. I mean doesn't the + sign show interaction between two entities in nature. ( BTW, I know this formula is wrong)

Forgive me, if it seems too childish a question to ask.

2. Jul 11, 2013

### HallsofIvy

You say you have no problem with "Force proportional to m" but ask why it is "multiplication"? Do you not understand that that is what "proportion" means? "A is proportional to B" means that A is equal to some constant times B: A= kB for some number B.

When we say that Galileo determined that "force is proportional to m", we mean that he measured the gravitational force on many different masses and found that ratio of force to mass was always a constant: F/m= k so that F= km. Of course, now we call that constant -g: "g" for "gravity". And it is negative because gravitational force acts downward.

The fact fact that it is a multiplication and not an addition is "experimental result".

3. Jul 11, 2013

### Naveen3456

Let's consider an experiment.

I push a small block (less weight) of wood on the floor of my room and I get some noise (sound waves/energy).

I push a bigger box sound energy is more.

If I keep on increasing the size of box, sound energy keeps on increasing.

1. Can I now say that size/weight of the box is directly proportional to the sound that I get. can I ever get a proportionality constant in this case, though these two things are proportional?

2. Can anybody tell me an example where interaction between two bodies is represented by a + sign?

4. Jul 11, 2013

### nasu

You don't know they are proportional until you actualy measure some parameter of the noise (level, intensity) and find out that the ratio between this parameter and the mass is constant.
The fact that the noise increases with mass does not automatically means proportional.

Of course, this is an imaginary experiment. In reality the noise can decrease with mass and it depends on many other parameters. Try to pull an empty can over the floor versus a heavy block of aluminum. Which one makes more noise?

The second question does not make sense to me.
The interaction is not represented by signs (plus or minus).
The interaction force can be attractive or repulsive but the sign depends on the axes you choose.

5. Jul 11, 2013

### DrewD

In reality, there are many additive terms in most forces. For example, a falling object feels the force of gravity, $-mg$ plus a drag force from the air, $c\rho Av^2$, where $\rho$ is the density of the air and $c$ is a constant that needs to be determined and $A$ is the area of the object that is perpendicular to the motion. So the two forces add and the total force is
$F=-mg+c\rho Av^2$

But, imagine if we had the force of gravity where $F_g=-(m+g)$. In this world, an object near the earth would accelerate as $a=-\frac{m+g}{m}$. If that were the case, very very light objects would accelerate extremely quickly. If the interaction were additive instead of proportional, the extreme case would be very weird.

I'm tempted to keep rambling on, but when you get down to it, physics is an experimental science. The theories are the way they are because that's the way they are.

6. Jul 11, 2013

### Staff: Mentor

You slipped on the "entities" vs "interaction" thing there, naveen: that equation is describing one INTERACTION, not one entity. One force. A plus sign would indicate considering multiple forces simultaneously, as drew said.

7. Jul 11, 2013

### dipole

Furthermore, it makes no sense to add mass and acceleration - they have different units! Mathematically we can write interactions by summing things which are the same kind of thing, but it doesn't make sense to say something like "mass and acceleration interact". Objects, which have mass, interact via forces. It doesn't make sense any other way.

8. Jul 11, 2013

### Staff: Mentor

Good point.

9. Jul 12, 2013

### Naveen3456

If speed and mass can 'interact' ( more the speed more the mass), why can't mass and acceleration interact.

Now, plz don't tell me that mass and speed don't interact via forces but via some yet undiscovered 'mechanism'.

I am talking about 'interaction' not about how it takes place, whether via forces or some other mechanism.

10. Jul 12, 2013

### Naveen3456

These two forces are acting 'simultaneously' on the body. This is a very complex situation. Mere addition of these forces should not give the real picture, IMHO.

Plz don't add gravity is not a force, I know it. I am posing this question in the context of what is quoted.

11. Jul 12, 2013

### Aero_UoP

Actually this is a quite simple situation. A complex situation is for example the shock wave/boundary layer interraction :P

To me, there is no point in asking "why multiplication and not addition" since multiplication IS addition... 4*5 = 5+5+5+5 or 4+4+4+4+4, the result is the same.

12. Jul 12, 2013

### dipole

Yes well words have specific meanings, and "interaction" has a specific meaning, whether you want it to or not. It is nonsense to say "speed and mass interact" because both speed and mass are properties of some object. Objects interact, quantities do not.

It's like saying that blue and round interact when describing a blueberry. Blueberries, however, can interact, very weakly through gravitation or by contact forces. Fields can also interact, but fields are physical things just like a blueberry is. This interaction, classically, is described in terms of forces. That's what physics is.

13. Jul 12, 2013

### Staff: Mentor

I think that you mean that relativistic mass (a deprecated concept) is a function of speed. That is a definition of the term "relativistic mass", where that term is defined as a function of speed. I cannot think of a definition of mass where acceleration is part of the definition.

The "interaction" as you call it, with speed and relativistic mass is simply a matter of definition and other terms are not defined the same way. It makes no sense to insist that the result of one definition apply to other definitions. Not only does acceleration not "interact" with speed, but other definitions of mass do not "interact" with speed. For instance, the invariant mass is completely independent of speed.

14. Jul 12, 2013

### DrewD

That is absolutely correct, but you don't need the quotations.
This is a simplified description, but it is quite good in air at moderate speeds. Physics doesn't get much simpler than this, so I'm confused about why you consider this a complex situation. Maybe I am misunderstanding what you consider complex.

If it is a rigid body that is symmetric so that there is no torque from the air resistance, addition of the vectors is sufficient.

It is my understanding that this conversation concerns classical forces, so gravity is a force.

dipole was saying that adding mass and acceleration does not make sense because the units do not match. There would have to be some sort of factor in front of each of them so that they add to be a force. It would be like saying,
"I walked one mile and then started to run at 6 mph. How far did I travel?"
It is not a well formed question.

15. Jul 13, 2013

### Naveen3456

Plz don't get irritated. It's not for the sake of argument, but I want to really understand things.

As per you, Mass and acceleration can be added again and again ( as multiplication is continued addition) but they can't be added once i.e. F=m+a is wrong.

'Why' is this so?

16. Jul 13, 2013

### Naveen3456

Thanks. That's what I meant by complex. So, it means that the formula is an approximation but not a complete picture of things.

Not arguing uselessly, I have heard that in quantum mechanics, interactions are more important than entities. In fact entities/objects are not considered to exist, until and unless they interact with the surroundings. It may be due to extremely small scale of things, but quantum mechanics experts say that it is infact the very truth of nature and size has not to do anything with it.

I know, we are considering a classical example, but still the concept of entities, interactions and forces seems to be somewhat arbitrary and even overlapping to my fragile brain.

For example, Dalespam said that invariant mass has nothing to do with speed, buy how would it even exist without the 'speed' of its constituent parts (like electrons, nucleons etc.) So, does it mean there are two kinds of 'speeds' for an object. One that deals with its internal structure and the other with its 'externality'( perhaps, I coined a new word) as a whole.

If we consider water instead of ball the 'internal' and 'external' speed seem to be dependent on/related to each other even if by a small amount.

BTW, this a bad example. Hope someone provides a better example.

17. Jul 13, 2013

### Aero_UoP

I don't get irritated. It just seems as if you're arguing just for the sake of arguement :p (and it's not just you, I've noticed that many users do so and I can't really understand why...)

18. Jul 13, 2013

### Aero_UoP

I think I agree with dipole...
I have another example too: black and round interact when describing... a blackberry! and if you put blue into the equation you have a blue blackberry, naveen! (at an excellent price too) :p lol
just kidding :p

19. Jul 13, 2013

### sophiecentaur

The reason that the two (adding and multiplying) are not the same in your example is because of the dimensions involved. Apples and pears do not add together because they are different entities. However, as part of the set 'fruit' (they both have the property of being a fruit), their numbers can quite reasonably be added together. BUT mass and the second time-differential of displacement have nothing in common (no property) and adding them together means nothing.

If you were interested in a quantity "applepears" then you could usefully multiply the number of apples by the number of pears ( as with man-hours and foot-pounds). You might have a hard time justifying this to anyone else, though.

Maths can only be used validly in Physics when it is a meaningful representation of a Physical situation. It is all too easy to write down nonsense expressions which are perfectly OK, Algebraically.

20. Jul 13, 2013

### Aero_UoP

Earlier, I tried to write a similar example (but with appricots and watermelons :P) explaining what you just said but at some point I found out that my English vocabulary needs some refreshing so I quit trying :P


text:
Notes On Bayes' Theorem - CBSE Class 12 Maths
The set of events E1, E2, E3, ..., En represents a partition of sample space S, if: • Ei ∩ Ej = ∅, i ≠ j , i, j = 1,2,3,...,n • E1 ∩ E2 ∩ E3 ∩...∩ En = S P(Ei) > 0 ∀ i = 1,2,3,...,n Theorem of Total Probability: Let {E1, E2, ... En} be a partition of sample space S, and suppose that each of the events E1, E2, ... En has non-zero probability of occurrence. Let A be any event associatedwith S.Then P(A) = P(E1)P(A|E1) + P(E2)P(A|E2) + ... + P(En)P(A|En) = ∑j=1n P(Ej)P(A|Ej) Proof: {E1, E2, ..., En} is a partition of sample space S. ∴ S = E1∩ E2∩ ... ∩ En Ei∪Ej = f, i ≠ j and i, j = 1, 2, 3, ..., n P (Ei) > 0 ∀ i = 1,2, 3, ..., n For any event A associated with S, A = A ∩ S = A ∩ (E1∪ E2∪ ... ∪ En) [∵ S = E1∪ E2∪ ... ∪ En] = (A ∩E1) ∪(A ∩E2) ∪ ... ∪(A ∩En) A ∩Eiis a subset of Eiand A ∩Ejis a subset of Ej. Given, Ei and Ej are disjoint for i ≠ j. ∴ A ∩Ei and A ∩Ej are also disjoint ∀i ≠ j and i, j = 1, 2, 3, ..., n. Thus, P(A) = P[(A ∩E1) ∪(A ∩E2) ∪ ... ∪(A ∩En)] = P(A ∩E1) + P(A ∩E2) + ... + P(A ∩En) By the multiplication rule of probability, P(A) = P(E1)P(A|E1) + P(E2)P(A|E2) + ... + P(En)P(A|En) P(A) = ∑j=1n P(Ej)P(A|Ej) Bayes' Theorem: If E1, E2, ..., En are n non empty events that constitute a partition of sample space S, i.e. E1, E2, ..., En are pair-wise disjoint and E1∪E2∪...∪En = S, and A is any event of non-zero probability, then P(Ei|A) = P(Ei)P(A|Ei) / ∑j=1n P(Ej)P(A|Ej) ∀ i = 1,2,3,......,n Proof: Given, E1, E2, ..., En is a partition of sample space S. ⇒ E1, E2, ..., En are pair-wise disjoint E1∪ E2∪... ∪ En = S By the formula of conditional probability, P(Ei|A) = P(A∩Ei)/P(A) = P(Ei)P(A|Ei) / P(A) [∵ P(A∩Ei) = P(Ei)P(A|Ei)] = P(Ei)P(A|Ei) / ∑j=1n P(Ej)P(A|Ej) [∵ P(A) = ∑j=1n P(Ej)P(A|Ej)] P(Ei|A) = P(Ei)P(A|Ei) / ∑j=1n P(Ej)P(A|Ej) ∀ i = 1,2,3,...., n Hence it is proved. Sometimes, Bayes' theorem is called the formula for the probability of causes. Events E1, E2, ..., En are called hypotheses. P(Ei) is called the priori probability of the hypothesis, Ei. The conditional probability, P(Ei|A), is called the posteriori probability of the hypothesis, Ei.

#### Summary

The set of events E1, E2, E3, ..., En represents a partition of sample space S, if: • Ei ∩ Ej = ∅, i ≠ j , i, j = 1,2,3,...,n • E1 ∩ E2 ∩ E3 ∩...∩ En = S P(Ei) > 0 ∀ i = 1,2,3,...,n Theorem of Total Probability: Let {E1, E2, ... En} be a partition of sample space S, and suppose that each of the events E1, E2, ... En has non-zero probability of occurrence. Let A be any event associatedwith S.Then P(A) = P(E1)P(A|E1) + P(E2)P(A|E2) + ... + P(En)P(A|En) = ∑j=1n P(Ej)P(A|Ej) Proof: {E1, E2, ..., En} is a partition of sample space S. ∴ S = E1∩ E2∩ ... ∩ En Ei∪Ej = f, i ≠ j and i, j = 1, 2, 3, ..., n P (Ei) > 0 ∀ i = 1,2, 3, ..., n For any event A associated with S, A = A ∩ S = A ∩ (E1∪ E2∪ ... ∪ En) [∵ S = E1∪ E2∪ ... ∪ En] = (A ∩E1) ∪(A ∩E2) ∪ ... ∪(A ∩En) A ∩Eiis a subset of Eiand A ∩Ejis a subset of Ej. Given, Ei and Ej are disjoint for i ≠ j. ∴ A ∩Ei and A ∩Ej are also disjoint ∀i ≠ j and i, j = 1, 2, 3, ..., n. Thus, P(A) = P[(A ∩E1) ∪(A ∩E2) ∪ ... ∪(A ∩En)] = P(A ∩E1) + P(A ∩E2) + ... + P(A ∩En) By the multiplication rule of probability, P(A) = P(E1)P(A|E1) + P(E2)P(A|E2) + ... + P(En)P(A|En) P(A) = ∑j=1n P(Ej)P(A|Ej) Bayes' Theorem: If E1, E2, ..., En are n non empty events that constitute a partition of sample space S, i.e. E1, E2, ..., En are pair-wise disjoint and E1∪E2∪...∪En = S, and A is any event of non-zero probability, then P(Ei|A) = P(Ei)P(A|Ei) / ∑j=1n P(Ej)P(A|Ej) ∀ i = 1,2,3,......,n Proof: Given, E1, E2, ..., En is a partition of sample space S. ⇒ E1, E2, ..., En are pair-wise disjoint E1∪ E2∪... ∪ En = S By the formula of conditional probability, P(Ei|A) = P(A∩Ei)/P(A) = P(Ei)P(A|Ei) / P(A) [∵ P(A∩Ei) = P(Ei)P(A|Ei)] = P(Ei)P(A|Ei) / ∑j=1n P(Ej)P(A|Ej) [∵ P(A) = ∑j=1n P(Ej)P(A|Ej)] P(Ei|A) = P(Ei)P(A|Ei) / ∑j=1n P(Ej)P(A|Ej) ∀ i = 1,2,3,...., n Hence it is proved. Sometimes, Bayes' theorem is called the formula for the probability of causes. Events E1, E2, ..., En are called hypotheses. P(Ei) is called the priori probability of the hypothesis, Ei. The conditional probability, P(Ei|A), is called the posteriori probability of the hypothesis, Ei.
Next


text:
Has been a couple of days since I started to try Rust. I was scared about the syntax which I found a little strange. I’m not a programmer, I’m an eletronics engineer that somehow learn to use Linux and code a bit and now is working as a Software development engineer.

My first touch with a programming language was with C when I was at high school, I made some projects in college with C and microcontrollers but nothing fancy. Some years later I met Python and did some projects for profit. After that I got my current job and know I use C/C++ and Python as my daily work.

So I live coding but without any serious background, I just like to learn new things and make some experiments. This year I started with Go which I found very interesting (I’ll post later about this) and started looking at Rust.

My first impression on Rust was that is a complicated language. The syntax looks weird and has too many symbols that I barely understand. When I was learning Go (I’m still learning…) I was reading more about Rust. The people that I admire and follow on Twitter were excited about Rust.

Mainly this post of Julia Evans about how start writing a simple Operating System on Rust was very exciting, so I decided to give a try.

## Things that I like about Rust (so far)

1. The community: A lot of people that likes open source works on their spare time. The people gathered around Rust seems to be the more passionated people of the open source community (maybe I’m overdoing this comment). The community is great, the support that you can found on the User forums is awesome. There is also a section called This week in Rust where a summary of blog posts, news, releases and other stuff is published every week.
2. The compiler: rustc is great, it’s very straightforward and gives you all the information that you need to continue your work. The compiler gives you hints on how to fix your compilation problems. Also, compilation is static so the deployment is very easy.
3. The dependency management: cargo is also a great tool. You just need to put a new dependency in a text file and cargo will download and install that dependency for your project.
4. The test suite capabilities: Test Driven Development is a must nowadays and with rust is very easy to do it. Just define a test and cargo test will handle the rest. I cannot find yet how to mock functions which is something required once you need to interact with external components within your tests, but there should be a way.
5. The memory management: I have read a couple of chapters of The book and now I’m in the ownership concept. What I understand so far is that only one binding (variable) can access to an allocated memory at the same time. This reduces race conditions. I have a lot to learn about this but looks very interesting.


text:
[Legenda] [Contentsof the thesis] [Comments on this module] [Legenda] [Contentsof the thesis] [Comments on this module]

## Quantitative interpretation with both Landau-Zener and rotational coupling=A08-m5bii2

Chemi-ionization in collisions between Na and I can be explained via crossing of the potential energy surfaces of the collisions . The Landau-Zener formula gives the transition probability between translationally coupled states. However, the Landau-Zener transition probability does not give an adequate quantitative explanation of the experimentally determined differential cross sections of the chemi-ionization process. It is likely that rotationally induced transitions could explain the discrepancy of measured and calculated differential cross section.

The discrepancy that the rotational coupling could explain is where the calculated cross section is too small for collisions with large impact parameters . Fig. A08-m5bii2-F1 clearly shows for increasing kinetic energy an increasing deviation of the relative differential cross section at  eV degree without rotational coupling. Even the relative cross sections more separated from the minimum would lead for a fitting procedure to an unphysical energy dependence of the Landau-Zener coupling parameter H12.
 Figure A08-m5bii2-F1: Smoothed differential cross sections for five different collision energies. (a), (b), (c), (d), (e): Full curves show the measured relative differential cross section, averaged over the interference structures. Absolute differential cross sections, calculated semi-classically and also averaged over the interference structure, have been given by the dashed curves. Use has been made of H12=0.05 eV. (f): At Ei = 29.7 eV the curves show the calculated differential cross section for H12=0.04, 0.05 and 0.07 eV

We have calculated the general shape of the differential cross sections of the chemi-ionization process again, now taking into account the rotational coupling .

Fig. A08-m5bii2-F2 gives again the measured general shapes of the differential cross sections at kinetic colliding energies of 13.1, 20.7, 29.7, 38.7 and 55.0 eV. A comparison has been made with calculated cross sections taking into account some rotational coupling.
 Figure A08-m5bii2-F2: Smoothed differential cross section for five different collision energies. (a), (b), (c), (d), (e): Full curves show the measured relative differential cross section, averaged over the interference structure. Dashed curves show calculated absolute cross sections using the coupling elements H12=0.0024 a.u. (0.065 eV): and H12>=0.04 a.u. (f): Effect of rotational coupling on the minimum of the differential cross section due to collisions with large collision parameters. Abscissa and ordinate scales have been extended by a factor of two with respect to the corresponding figure (e).

Indeed, the minimum in the differential cross section has been increased to a degree dependent on the kinetic energy.

Moreover, it is very obvious that now it is possible to find one set of coupling constants giving a good fit of measured and calculated cross sections for all energies. This set consists of the values H12=0.065 eV and Hrot=3 x 10-17 eV corresponding to the values of 0.0024 a.u. and 0.04 a.u., respectively.

A comparison of the corresponding cross section curves of Fig. A08-m5bii2-F1 and Fig. A08-m5bii2-F2 shows that rotational coupling at low kinetic energies increases the differential cross section only at the very minimum but for higher kinetic energies there is a rise over a larger -range. This feature makes it possible to use only one value of H12.

On the range  eV degree Fig. 0.2f gives the dependence of the cross section on some values of rot at Ei = 55  eV. For increasing coupling constant, the maximum contribution of rotational coupling to chemi-ionization moves to collisions with smaller impact parameters.

It must be noted that for impact parameters Eq. (E1)
 (E1)
does not hold any more because a sufficient separation is supposed between the classical turning point and the crossing point Rc. (A similar remark to the Landau-Zener coupling has been made in A08-m5bii1 , point D.) For an incomplete passage of the transition region around Rc Eq. (E1) gives too large a value of Pb,rot. In the present case with the parameters used the resulting effect is the product Pb,rot(1-Pb,rot), too small for collisions with Ei = 55  eV and and too large for the corresponding collisions at Ei = 13.1 eV. Indeed, a correction to this effect should improve the agreement of measured and calculated curves of Fig. F2a and Fig. 2c. It is suspected that the remaining apparent discrepancy of the relative intensities at  eV degree is due to convolution effects, measuring faults and the improper use of Eq. (E1) for .

Reliability
The estimated value H12=0.065 eV differs rather much from the value of 0.05 eV, estimated from total cross-section measurements on the collision energy range 2-20 eV. The effect of these two values on the absolute differential cross section can be observed from Fig. 0.1 (H12=0.05 eV) and Fig. 0.2 (H12=0.065 eV). At Ei = 55  eV the cross sections of Fig. F2 have hardly different values, while at Ei = 13.1  eV the cross sections differ by a factor of two. Of course, relative measurements on the differential cross section versus the kinetic energy should give a hint to the correct value of H12. However, at the present measurements it is impossible to distinguish in this way these values of H12. It is expected that the surface-ionization detector as well as the scattered-ion detector have large and unknown energy-dependent efficiencies.


text:
# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#4

Question Functions  and  are defined by  for .      i.       Find the range of .    ii.       Sketch the graph of .   iii.       State, with a reason, whether  has an inverse. Solution i.   We have the function; We can write it as; We know that; Hereby; We can find the range of   by substituting extreme possible values of ; Therefore; ii.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#10

Question i.       The diagram shows the line  and the curve , which intersect at the points A and B. Find a.   the x-coordinates of A and B, b.   the equation of the tangent to the curve at B, c.   the acute angle, in degrees correct to 1 decimal place, between this tangent and the line .    ii.       Determine […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#9

Question The diagram shows a rectangle . The point  is  and  is . The diagonal  is parallel to the x-axis.     i.       Explain why the y-coordinate of  is 6. The x-coordinate of  is .    ii.       Express the gradients of  and  in terms of .   iii.       Calculate the x-coordinates of  and .   iv.       Calculate the area of the rectangle . Solution i.   Consider the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#7

Question A piece of wire of length 50 cm is bent to form the perimeter of a sector POQ of a circle. The radius of the circle is r cm and the angle POQ is q radians (see diagram). i.       Express  in terms of r and show that the area, Acm2, of the sector is given by    .    […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#6

Question In the diagram, OABCDEFG is a cube in which each side has length 6. Unit vectors ,  and  are parallel to ,  and  respectively. The point  is such that   and the point  is the mid-point of . i.       Express each of the vectors  and  in terms of ,  and .    ii.       Find the angle OQP. Solution i.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#1

Question The equation of a curve is such that  . Given that the curve passes through the point (4, 6), find the equation of the curve. Solution We can find equation of the curve from its derivative through integration; For the given case; Therefore; Rule for integration of  is: Rule for integration of  is: Rule for integration of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#5

Question i.               Prove the identity . ii.               Solve the equation  for . Solution i.   We have the trigonometric identity; We can rewrite it in two ways; ii.   To solve the equation  for , we can express, as demonstrated in (i), the right hand side of given equation as; Therefore the given equation can be written as; We have […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#8

Question The function  is such that  for ,      i.       Obtain an expression for  and explain why  is a decreasing function.    ii.       Obtain an expression for .   iii.       A curve has the equation . Find the volume obtained when the region bounded by the curve, the coordinate axes and the line is rotated through  about the x-axis. Solution i.   We have the function; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#2

Question i.   Find, in terms of the non-zero constant ,  the first four terms in the expansion of  in ascending powers of .    ii.     Given that the coefficients of  and  in this expansion are equal, find the value of . Solution i.   Expression for the Binomial expansion of  is: In the given case: Hence; ii.   Since the coefficients […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#3

Question A progression has a second term of 96 and a fourth term of 54. Find the first term of the progression  in each of the following cases:     i.       the progression is arithmetic,    ii.       the progression is geometric with a positive common ratio. Solution i.   From the given information, we can compile following data for Arithmetic Progression (A.P); Expression for […]


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# Math Help - i have four math problems i have been struggling with for a while now

1. ## i have four math problems i have been struggling with for a while now

Questions 1,2: using rational theorem + descartes's rule of sign to determine possible rational & real zeroes. find all zeroes & express the polynomial as a product of linear factors. sketch the graph of the function, indicating all intercepts. estimate turning points.
1. f(x) = 3x^3 + 2x^2 - 19x + 6
2. f(x) = X^4 - 3x^3 + 6x^2 - 12x + 8

Question 3: a company manufactures scooters and estimates profit depending on advertising expenses using the function: f(x) = -.25x^2 + 20x + 100
what expense in advertising will yield the maximum profit? what would the profit be?

Question 4: i could not past the graph on this problem i hope that does not cause any problems.
the graph above indicates the recent anticipated rise in global precipitation as greenhouse gases increase over time. selecting the coordinates (200,2) and (2050,4), write a linear function that would enable us to predict the % increase by 2150.

again it is greatly appreciated to all you are willing to help me with these four questions.

2. Originally Posted by jiozzio
Questions 1,2: using rational theorem + descartes's rule of sign to determine possible rational & real zeroes. find all zeroes & express the polynomial as a product of linear factors. sketch the graph of the function, indicating all intercepts. estimate turning points.
1. f(x) = 3x^3 + 2x^2 - 19x + 6
Descarte's rule of signs say that this either 0 or 2 positive roots and one negative root. The "rational root theorem" tells you that the only possible rational roots are $\pm 1$ and $\pm 2$. Have you tried those?

2. f(x) = X^4 - 3x^3 + 6x^2 - 12x + 8
Descarte's rule of signs tells you that this has no negative roots. The "rational root theorem" tells you that any roots must be 1, 2, 4, or 8. Try them.

Question 3: a company manufactures scooters and estimates profit depending on advertising expenses using the function: f(x) = -.25x^2 + 20x + 100
what expense in advertising will yield the maximum profit? what would the profit be?
f(x)= -.25(x^2- 80x)+ 100. 80/2= 40 and 40^2= 1600 so, completing the square, f(x)= -.25(x^2- 80x+ 1600- 1600)+ 100= -.25(x^2- 80x+ 1600)+ 400+ 100= -.25(x- 40)^2+ 500.

Since a square is never negative but multiplying by -.25 means -.25(x- 40)^2 is never positive, that is always "500 minus something". It will never be larger than 500 but will be equal to 500 when x= 40.

Question 4: i could not past the graph on this problem i hope that does not cause any problems.
the graph above indicates the recent anticipated rise in global precipitation as greenhouse gases increase over time. selecting the coordinates (200,2) and (2050,4), write a linear function that would enable us to predict the % increase by 2150.
Those look like years. I am going to assume that "200" was supposed to be "2000". A linear function is of the form y= ax+ b. Since it passes through (2000, 2), x= 2000, y= 2 satisfies that equation. Since it passes through (2050, 4), x= 2050, y= 4 satisfies that equation.

That means we have 2= 2000a+ b and 4= 2050a+ b. Solve those equations for a and b (subtracting one equation from the other immediately eliminates b). Once you have found a and b, evaluate ax+ b for x= 2150.

again it is greatly appreciated to all you are willing to help me with these four questions.