Matrix elimination

Matrix elimination is a fundamental operation that can be used for many purposes, such as solving a system $$Ax=b$$, computing the rank of a matrix or computing the inverse of a matrix. There are two main types of matrix elimination: Gauss elimination and Gauss-Jordan elimination.

Gauss Elimination
Gauss elimination aims to bring a matrix in to a row echelon form, i.e., A form like $$ \begin{matrix} \asterisk \end{matrix} $$