Question: 1. Given the following matrix: 1 -2 -3 4 5 6 1-7 9-111 (a) Find this matrix's determinant by hand (10 Points). (b) Based upon

1. Given the following matrix: 1 -2 -3 4 5 6

1. Given the following matrix: 1 -2 -3 4 5 6 1-7 9-111 (a) Find this matrix's determinant by hand (10 Points). (b) Based upon your answer for (a), how do you know that this matrix has an inverse (3 Points)? (e) Find this matrix's inverse by hand showing all steps (15 Points). (d) Use your answer from (e) to solve the following set of simultaneous equations (6 Points): 4+ 5y + 62 = 2 -7x +9y - 112 = 4 -x - 2y - 32 = 6 2. The following equation y = ln(2x) + x2 5x + 4 has been graphed for you (please below): 5 4 In(2x)=x-3x+4 3 2 1 0 -1 -2 -3 4 2 As shown this equation has two roots. (a) Use the Newton-Raphson method with a starting point of 1.0 to solve for the root on the left using 2 iterations. Include an estimate for the error as well (16.5 Points). (b) Use the False Position method with a starting range of [3.0 4.0) to solve for the root on the right using 2 iterations, Include an estimate for the error as well (16.5 Points)

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