Question 4 A system is defined by the differential equations: * 1 = X2 *2 =-14x, - 9x2 (a) Write the system state equation in the form: X = AX , where X = X 2 (2 marks) (b) Show that the eigenvalues of A are 1, = -2, and 12 = -7. (3 marks) (c) Derive the resultant eigenvectors of A, and hence construct the spectral matrix, S, and the modal matrix, M (6 marks) (d) Determine the transition matrix: ed = MeS'M-', given: est = 0 (6 marks) (e) Hence, determine expressions for the zero-input time response, x1 (t) and x2 (t), assuming the initial conditions: x1 (0) = 1; X2 (0) = 0 (8 marks)