LU Decomposition

Definiiton

$\mathbf{A}={\mathbf{E}}^{-1}\mathbf{U}=\mathbf{LU}$ where $\mathbf{E}$ is the lower triangular matrix of Gauss Elimination^[History of G.E] and $\mathbf{U}$ is the result upper triangular matrix of Gauss Elimination^[Result of G.E].