Java

Matrices are fundamental objects in computer science and mathematics alike, they are used extensively in computer graphics, error correcting codes, Google's pageRank algorithms, differential equations and many more. In this assignment you are asked to create the following set of methods dealing with matrix manipulation: 1. a method that given two m times n matrices A and B returns their sum A + B. 2. a method that given two m times n matrices A and B returns their difference A - B. 3. a method that given an m times n matrix A and a scalar r returns their product rA. 4. a method that given an m times n matrix A and an n times p matrix B returns their product AB. 5. a method that given an m times n matrix A returns its transpose AT. 6. a method that verifies wheat her a given n time n matrix A is symmetric. 7. a method that given an n times n matrix A and a positive integer k computes A^k. 8. (HONORS) a method that given a nilpotent matrix N computes e^N. 9. (HONORS) a method that given an n times n A computes its determinant. 10. (HONORS) a method that given anon-singular n times n matrix A and an n-dimensional column vector b solves the equation Ax = b using Cramer's rule. Example Define A = [1 4 2 5 3 6] B = [-1 9 4 8 7 2] C = [2 5 4 1 3 7] D = [1 3 2 4]