Let A be the matrix 1 1 1 -2 0-3 4 0 6.5 (a) Let =...

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Let A be the matrix 1 1 1 -2 0-3 4 0 6.5 (a) Let = [100], = [010] and d = [001]. Use Gauss-Jordan elimination, solve the three equations Ax = 6, Ay = and Az = d to find x, y and z. (b) Hence, or otherwise, find A-1. (c) Find ||A||, ||A-1|| and the condition number of A, all based on on the induced ₁ norm. (d) The dose of three different medicines to be given to a patient is given by a vector d. To find d, a computer solves the equation Ad=h, where h is some measurements about the patient's health. There could be a 1% relative error in h, however the medicines are also quite safe and even if you give the patient double the optimal dose, it should still be safe. Do a calculation to decide how happy you would be to use such a system. Would you make any recommendations to the person writing the computer code? Let A be the matrix 1 1 1 -2 0-3 4 0 6.5 (a) Let = [100], = [010] and d = [001]. Use Gauss-Jordan elimination, solve the three equations Ax = 6, Ay = and Az = d to find x, y and z. (b) Hence, or otherwise, find A-1. (c) Find ||A||, ||A-1|| and the condition number of A, all based on on the induced ₁ norm. (d) The dose of three different medicines to be given to a patient is given by a vector d. To find d, a computer solves the equation Ad=h, where h is some measurements about the patient's health. There could be a 1% relative error in h, however the medicines are also quite safe and even if you give the patient double the optimal dose, it should still be safe. Do a calculation to decide how happy you would be to use such a system. Would you make any recommendations to the person writing the computer code?