State Space Control Theory Controllability/Observability

[ccmuggs13]

I'm studying for an upcoming final and this is a question from a practice exam we were given. It looks simple but for some reason I just can't wrap my brain around it. The question is attached and gives a state space representation of a system (A, B, C matrices) and asks what part of the system is controllable, observable, both and neither. It is clear from the zeros in the B and C matrices that the system as a whole is neither controllable nor observable, but I am not entirely sure what it means as far as the "parts" of the system that are controllable or observable.

 

[donpacino]

It is clear from the zeros in the B and C matrices that the system as a whole is neither controllable nor observable, but I am not entirely sure what it means as far as the "parts" of the system that are controllable or observable.

A system can be 100% controllable with some of the B matrix being zero.
the same can be said for a system with some of the C matrix being zero.

why don't you start by computing the controlability and observability matrices.