A dynamic system is described by the state-variable equations x = A x x = A x and y = C x y

A dynamic system is described by the state-variable equations $\dot{x}=Ax$ and $y=Cx$, where

(a) Obtain the State-Transition Matrix $\Phi \left(t\right)$.

(b) Find the state variable responses $x_1\left(t\right)$ and $x_2\left(t\right)$.

(c) Find the output response $y\left(t\right)$.

(d) For this system verify that:

A 1 1 0 -2 andx(0)=[12]". C = [2 -1]