Eroxl's Notes
Gaussian Elimination
aliases
Row Reduction

Gaussian elimination is an algorithm for solving linear systems. Gaussian elimination consists of a sequence of elementary row operations performed such that the resulting left side of the equation is the identity matrix of the same size.

This is true because

This means that

where 's are the constants we're solving for and 's are the variables.

Example of the Algorithm

Given the following linear system

Row Operations System of Equations Augmented Matrix

This means that in this example , , and