The aim of this question is to assess your understanding of elementary matrices and the LU decomposition of a matrix. (a) Determine, by hand, the elementary matrices Eįj that represent the elementary row operations used in applying Gaussian elimination to the matrix A = -1 3 -31 3 4 5 2 -1 8 - to transform A to upper triangular form. (b) Deduce the LU decomposition of A, and use it to solve the following system of linear equations. -x₁ + 3x₂ − 3x3 = = 14, 3x14x2 + 5x3 = -23, 2x1 x₂ + 8x3 = -15.

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