2. (25 points) (a) With A an x matrix and Bm consider the following controlled inhomogeneous system 2 Ay+B+ft) on (T) (2) 3 = 90 where f(t) is a vector-valued-function of time. Assume that the system is controllable at time I for the homogeneous case f = 0. Under this assumption describe carefully how, given arbitrary YT ER one can find a control 22 such that the corresponding solution of (2). satisfies y (7) =YT (b) In (2). take A B 04 fit= y (0) = ei, T = 1. Therewith, find control a such that the corresponding solution y(t) of (2) satisfies y(1) = [0,0]7. (Note: your solution must involve the Gramian matrix for the possibility of credit.)