(a) Given that the matrix T-2 -2 -21 A = 6 -2 -6 -6 -2 21...

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(a) Given that the matrix T-2 -2 -21 A = 6 -2 -6 -6 -2 21 may be decomposed as follows: [-2 -2 -21 6 -2 -6 [-6 -2 -21 0 -8 -12 21 1 -2 -2 = |-3 2] 1 3 -0.5 1ll o Hence evaluate the determinant of A , showing the steps in your calculations clearly. (i) (2 marks) (ii) Hence solve the systems Ax = b k = 1,2,3 where b, = b2 = 1 and b3 0. Show the steps in your calculations %3D clearly. (10 marks) (iii) Use the results of part (ii) to write down the inverse of A, stating how your answer has been constructed. (2 marks) (b) The following non-linear system is to be solved numerically using Newton's method: 5x,? – 6x, + x,3 – 16 = 0 X1x22 - x2 - 6 = 0 Perform one iteration, starting from (1,1)". Show the steps in your calculations clearly. (6 marks) (a) Given that the matrix T-2 -2 -21 A = 6 -2 -6 -6 -2 21 may be decomposed as follows: [-2 -2 -21 6 -2 -6 [-6 -2 -21 0 -8 -12 21 1 -2 -2 = |-3 2] 1 3 -0.5 1ll o Hence evaluate the determinant of A , showing the steps in your calculations clearly. (i) (2 marks) (ii) Hence solve the systems Ax = b k = 1,2,3 where b, = b2 = 1 and b3 0. Show the steps in your calculations %3D clearly. (10 marks) (iii) Use the results of part (ii) to write down the inverse of A, stating how your answer has been constructed. (2 marks) (b) The following non-linear system is to be solved numerically using Newton's method: 5x,? – 6x, + x,3 – 16 = 0 X1x22 - x2 - 6 = 0 Perform one iteration, starting from (1,1)". Show the steps in your calculations clearly. (6 marks)