2. Consider the following state-space system representation. 0 10 0 dz 0 01 z+0u dt -2 3 5 y=[100]z a) Determine if the system is controllable. b) If so, find its controllable canonical form. c) Determine the coordinate transform = Tx for the controllable canonical system. d) Use the formulations of the characteristic equation to determine the gain matrix K for a controller producing the system dynamics with eigenvalues of -1, -3, and -7. e) Use the formulations of the characteristic equation to determine the gain matrix K for a controller producing the system dynamics with eigenvalues of -1, -2+5j. 3. Repeat problem 2d using the generalized (Acker's) solution. 4. Is it possible to use the generalized (Acker's) solution to determine state feedback gains if the desired eigenvalues contain imaginary components?