Automated function to solve Ax=b showing all matrix transformations at each step

by Nasser M. Abbasi

Introduction

This function runs inside Mathematica. It accepts matrix A and vector b, and solves Ax=b for x, showing each step all the Gaussian eliminations steps made, all the way to the Reduced Echelon form. This works only on matrices with non-zero determinant. Examples below are shown from textbook Differential equations and linear Algebra, 3rd edition by Edwards and Penney.

Example of usage and how to call the function

Section 3.1, problem 11

Section 3.1, problem 21

Section 3.2, problem 11

Section 3.2, problem 24

Section 3.2, problem 27

Section 3.3, problem 8

Section 3.3, problem 32

Example 7, page 105

Example 2, page 169

problem 1, page 175

problem 2, page 175