A third order system, namely, X = AX [a11 a12 a13] [x1] x2 =a21 a2z a23...

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A third order system, namely, X = AX [a11 a12 a13] [x1] x2 =a21 a2z a23 x2 a31 a32 a33] [x3] has system matrix, 0 1 0 A = -1 -1 -2 -3 1 -4] Initial conditions on the states are: x (0) = -1; x2(0) = 0; x3 (0) = 0 a) Derive a primitive block diagram that defines this system. (30 marks) b) Determine the eigenvalues of A, and hence nominate the eigenvectors. (15 marks) c) Construct the modal (M), and spectral (S) matrices. (5 marks) d) Hence, determine the state responses to the initial conditions. (30 marks) e) Cross-check the x2 and x3 responses obtained above, by performing appropriate operations on the x response. (20 marks) A third order system, namely, X = AX [a11 a12 a13] [x1] x2 =a21 a2z a23 x2 a31 a32 a33] [x3] has system matrix, 0 1 0 A = -1 -1 -2 -3 1 -4] Initial conditions on the states are: x (0) = -1; x2(0) = 0; x3 (0) = 0 a) Derive a primitive block diagram that defines this system. (30 marks) b) Determine the eigenvalues of A, and hence nominate the eigenvectors. (15 marks) c) Construct the modal (M), and spectral (S) matrices. (5 marks) d) Hence, determine the state responses to the initial conditions. (30 marks) e) Cross-check the x2 and x3 responses obtained above, by performing appropriate operations on the x response. (20 marks)