I need help with the following multiple-choice, thank you in advance!

Problem 6: The matrices [2 2 1 [5 14 13 A = 1 3 1 and B = 0 1 0 1 2 2 0 0 1 are similar because ANS: (a) they have the same value of trace (b) they have the same eigenvalues (c) there is a nonsingular matrix P which satisfies B = P-1AP (d) all of the above dt2 dt Problem 7: Consider a multivariable system which is described by differential equations dy(t) dyi(t) + 5 - 3y2 (t) + y;(t) = u(t) + + 2uzt) dy(t) dyz (t) + y(t) + 3y2 (t) = uz(t) dt dt How many state variables are required to defined the system? ANS: (a) 2 + 2 (b) 3 (c) 4 (d) 5 Problem 8: What properties of a state space model will be invariant under the similarity transformation? ANS: (a) transfer function (b) eigenvalues (c) characteristic equation (d) all of the aboe