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@jemoka / Jemoka Knowledge Base / wiki/concepts/gaussian_elimination.md
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--- title: "Gaussian elimination" type: concept related: [Gaussian Elimination] source: https://www.jemoka.com/posts/kbhgaussian_elimination/ confidence: high status: active --- The point of Gaussian elimination is to solve/identiy-ify a linear equation. Take, if you have a matrix expression: \begin{equation} Ax = b \end{equation} We can apply \(A^{-1}\) to both side, we then have: \begin{equation} A^{-1}Ax = A^{-1} b \end{equation} Applying the definition of the identity: \begin{equation} Ix = A^{-1}b \end{equation} Therefore, to solve for some \(A^{-1}\), which would yield \(x\).