Given the system in state equation form,

\[\frac{d \mathbf{x}(t)}{d t}=\mathbf{A} \mathbf{x}(t)+\mathbf{B} u(t)\]

where

(a) \(\mathbf{A}=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & -3 & 0 \\ 0 & 0 & -2\end{array}ight]\)

\(\mathbf{B}=\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}ight]\)

(b) \(\mathbf{A}=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 3\end{array}ight]\)

\(\mathbf{B}=\left[\begin{array}{l}0 \\ 1 \\ 1\end{array}ight]\)