Consider the system described by the state equations (a) Find the state transit...

Consider the system described by the state equations

(a) Find the state transition matrix.

(b) Verify the results of part (a), using the series of (8.36).

(c) Find the initial-condition response for x(0) = [12]^T.

(d) Verify the calculation of the state vector x(t) in part (c), by substitution in the equation x(t) = Ax(t).

(e) Calculate the system unit step response, with x(0) = 0, using (8.28) and y(t) = Cx(t) + Du(t).

(f) Verify the results of part (e), using the system-transfer function and the Laplace transform.

(g) Verify the results of parts (c) and (e), using SIMULINK.