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# 5: Gaussian Elimination


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.

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