# 5: Gaussian Elimination

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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.

This page titled 5: Gaussian Elimination is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Y. D. Chong via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.