How do I approach this?

Obtain a combined controllability /observability decomposition for the LTI system i = Ax + Bu, y = Cx by following these steps: a) Ignoring the control for now, write down the Kalman observability decomposition. b) Now add the control, noting that the B matrix assumes no special structure in the coordinates that give the observability decomposition.c) For the observable part of the system, switch coordinates to get the Kalman controllability decom- position for it. Repeat separately for the unobservable part. d) Write the combined controllability /observability decomposition of the system in the following form: Boc * Coc Aoc Ao12 ** 0 Coc u, Coc * + Aoc * 0 Boc Coc 0 Aoc Ao12 Coc 0 Coc Coc 0 0 Aoc O Coc Coc Coc y = 0 0 Coc Coc ] Coc Coc Identify four types of modes: controllable and observable, uncontrollable but observable, controllable but unobservable, and uncontrollable and unobservable