Use the Gauss-Siedel method to approximate the solution of the following system of linear equations. (Hint: you can stop iteration when you get very close results in three decimal places.) 5x1 - 2x2 + 3x3 = -1 %3D -3x1 + 9x2 + X3 = 2 2x1- x2-7x3 = 3

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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.