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decomposition of the coefficient matrix is: A = LU = [ 3 2 -1 ] [ 2 -2 4 ] [-1 0.5 -1 ] L = [ 1 0 0 ] [ 0.67 1 0 ] [-0.33 0.2 1 ] U = [ 3 2 -1 ] [ 0 -3.33 4.67] [ 0 0 QR Decomposition QR decomposition is a method to decompose a matrix into an orthogonal matrix and an upper triangular matrix. This