1) Controllability and observability for SISO systems in Jordan form. a) 25 points Let J= 10 11 , B = |b2, C= |cz cz cz/ 0 0 Find necessary and sufficient conditions on the entries b; and c; for the pairs (J, B) and (CJ) to be respectively controllable and observable. b) 25 points Repeat for J= 0 0 0 0 c) 25 points Generalize to an arbitrary Jordan block. 1) Controllability and observability for SISO systems in Jordan form. a) 25 points Let J= 10 11 , B = |b2, C= |cz cz cz/ 0 0 Find necessary and sufficient conditions on the entries b; and c; for the pairs (J, B) and (CJ) to be respectively controllable and observable. b) 25 points Repeat for J= 0 0 0 0 c) 25 points Generalize to an arbitrary Jordan block