Application 4 Table of Contents
Description of Tasks
Task 1
Implement a method that returns the scalar multiple of a given matrix. Add an entry to your software manual documenting the method.
Task 2
Implement a method that returns the sum of two matrices of the same size. Add an entry to your software manual that documents the method.
Task 3
Implement a method that will return the outer product of two vectors. Add an entry to your software manual documenting the method.
Task 4
Implement a method that will compute the solution of a square linear system of equations where the coefficient matrix is a diagonal matrix.
Task 5
Implement a method that will compute the solution of a square linear system of equations where the coefficient matrix is upper triangular. Document this backsubstitution method in a software manual entry.
Task 6
Implement a method that will compute the solution of a square linear system of equations where the coefficient matrix is lower triangular. Document this backsubstitution method in a software manual entry.
Task 7
Implement a method that will perform elementary row operations on a matrix to take the matrix to row echelon form. The resulting matrix should be upper triangular through the rows. If the matrix is not a square matrix, define an appropriate output for the method tha will return the row echelon form. Add an entry to your software manual documenting the method.
Task 8
Using previous methods you have created, write a code that will solve a square linear system of equations using Gaussian elimination (elementary row operations) to reduce the augmented coefficient matrix to row echelon form and then apply backsubstitution to determine an approximate solution for the linear system.
Task 9
Write a routine that will generate a symmetric diagonally dominant matrix that has real values in all entries of the matrix. Add an entry to your for the method you create.
Task 10
Search the internet for sites that discuss parallel algorithms for matrix-vector multiplication and matrix-matrix multiplication. Summarize in a paragraph or two and as always, cite your sites.