Gaussian Elimination for Solving Linear Systems
Gaussian elimination solves systems of linear equations in $O(n^3)$ time. Consider a system of $n$ linear equations in $n$ unknowns: $$ a_{11}x_1 + a_{12}x_2 + \cdots + a_{1n}x_n = b_1 $$ $$ \vdots $$ $$ a_{n1}x_1 + a_{n2}x_2 + \cdots + a_{nn}x_n = b_n $$ Gauss-Jordan Elimination Algorithm: Select a...