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For the system shown

`x^(˙)=[[0,2],[-3,-5]]x+[[1],[2]]u,y=[[1,1]]x,[[x_(1)(0)],[x_(2)(0)]]=[[0],[0]], and u(t)=0`

(a) Obtain

`e^(At)`

using Cayley-Hamilton. (b) Obtain

`e^(At)`

by first finding

`(sI-A)^(-1)=\Phi (s)`

. (c) Evaluate

`x(t)`

and

`y(t)`

using time domain approach. (d) Evaluate impulse response of the system,

`h(t)`

. (e) Evaluate

`x(t)`

by first obtaining

`x(s)`

. (f) Evaluate system transfer function

`H(s)`

.