Instructions

• Use python programming language.
• By random entries, I mean a system generated random number.
• Also share the screenshot of running code with a valid example

Finding solutions of linear systems

a) Write a code taking as input a matrix A of size m n and a vector b of size m 1, where m and n are arbitrarily large numbers and m < n, constructing the augmented matrix and performing

• REF, and
• RREF

without using any built-in functions. In case you encounter any division by 0, you can choose a different A and/or b.

Deliverables: The code snippet showing the procedure for REF and RREF. screenshot of running code with a valid example

b) Identify the pivot and non-pivot columns and find the particular solution and solutions to Ax = 0.

Deliverables: The code snippet showing the pivot and non-pivot columns, particular solution and the solutions to Ax = 0. screenshot of running code with a valid example

c) Consider a random 5 7 matrix A and a suitable b and show the REF, RREF, pivot columns, non-pivot columns, the particular solution, the solutions to Ax = 0, the general solution and verify the general solution.

Deliverables: The random matrix A, vector b and other quantities mentioned in the question. screenshot of running code with a valid example