FConsider the following continuous-time linear time-invariant system x_ (t) = 2 4 0 1 0 1 0 0 0 0 0 3 5 | {z } A x(t) + 2 4 1 1 1 3 5 |{z} B u(t); y(t) = 1 1 1 | {z } C x(t): Note that A has eigenvalues f1; 0; 1g. (a) Is the system controllable? What is its reachable subspace? (b) Determine the controllability for each of the three modes of the system. (c) Suppose x(0) = 1 2 1 T and u(t) 1 for t 0. Find y(t) for all t 0.