# 5: Gaussian Elimination

- Page ID
- 34833

This article discusses the **Gaussian elimination** algorithm, one of the most fundamental and important numerical algorithms of all time. It is used to solve linear equations of the form

\[\mathbf{A} \vec{x} = \vec{b},\]

where \(\mathbf{A}\) is a known \(N\times N\) matrix, \(\vec{b}\) is a known vector of length \(N\), and \(\vec{x}\) is an unknown vector of length \(N\). The goal is to find \(\vec{x}\). The Gaussian elimination algorithm is implemented by Scipy's `scipy.linalg.solve`

function.