Program (in a Python function; hint: extend the function from Assignment 1) a (mxm) LU factorization algorithm (using partial pivoting) for a matrix A and compute the PLU factors. The factorization is obtained by elimination steps k = 1,...,m-1 so that A-₁AV -k+1,...,m and where the multipliers mix are given by mi When km-1, A, is upper triangular, that is, U₁ = A). The lower triangular matrix is obtained using the multipliers m.,. that is Lij = mij Vi>j. Li,i = 1, and Lij = 0 Vi

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LUP Decomposition

LU decomposition stands for Lower-Upper decomposition. LU decomposition is the factorization of the lower triangular matrix and an upper triangular matrix. It is very useful in linear algebra and numerical analysis. A permutation matrix is usually included in the product. Gaussian elimination in a matrix form is known as LU decomposition, When inverting a matrix or evaluating its determinant, this is a crucial step. Tadeusz Banachiewicz, a Polish mathematician, first proposed the LU decomposition in 1938.