$$\require{cancel}$$
$\mathbf{A} \vec{x} = \vec{b},$
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.