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.
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