Question 5 Consider the following system of linear equations (2x1 + 3x2 + 4x3 = 12 - 2x1 x2+3x3 = 3 4x1-2x2 + x3 = 1 (a) Write down matrix A and vector b, where Ax = b. Apply the LU decomposition technique on A. Find the elementary matrices Eij. (5 marks) (b) Based on the LU decomposition of A, solve the system of linear equations. (3 marks) (c) Use the LU decomposition of A to find the first column of A-¹. (2 marks)

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