For a system that has two state variables such that \(\mathbf{x}(\mathbf{t})=\left[\begin{array}{ll}x_{1} & x_{2}\end{array}ight]^{T}, \mathbf{x}(\mathbf{0})=\left[\begin{array}{ll}1 & 1\end{array}ight]^{T}\) and

\[A=\left[\begin{array}{cc}0 & 1 \\-2 & -3\end{array}ight]\]

find the state variable responses \(x_{1}(t)\) and \(x_{2}(t)\).

\[\begin{aligned}
& x_{1}(t)=3 e^{-t}-2 e^{-2 t} \\
& x_{2}(t)=-3 e^{-t}+4 e^{-2 t} .
\end{aligned}
\]