Find the state response and system response for the systems described as follows:

(a) \(\left[\begin{array}{l}\dot{x}_{1} \\ \dot{x}_{2}\end{array}ight]=\left[\begin{array}{ll}-4 & 1 \\ -3 & 0\end{array}ight]\left[\begin{array}{l}x_{1} \\ x_{2}\end{array}ight]+\left[\begin{array}{l}1 \\ 0\end{array}ight] r\)

\[
y=\left[\begin{array}{ll}
1 & 0
\end{array}ight]\left[\begin{array}{l}
x_{1} \\
x_{2}
\end{array}ight], \quad\left[\begin{array}{l}
x_{1}(0) \\
x_{2}(0)
\end{array}ight]=\left[\begin{array}{l}
0 \\
0
\end{array}ight], \quad r(t)=\delta(t), \text { unit impulse }
\]

(b) \(\left[\begin{array}{l}\dot{x}_{1} \\ \dot{x}_{2} \\ \dot{x}_{3}\end{array}ight]=\left[\begin{array}{rrr}-3 & 1 & 0 \\ -2 & 0 & 1 \\ 0 & 0 & 0\end{array}ight]\left[\begin{array}{l}x_{1} \\ x_{2} \\ x_{3}\end{array}ight]+\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}ight] r\)

\[
\left[\begin{array}{l}
y_{1} \\
y_{2}
\end{array}ight]=\left[\begin{array}{lll}
1 & 0 & 1 \\
0 & 0 & 1
\end{array}ight]\left[\begin{array}{l}
x_{1} \\
x_{2} \\
x_{3}
\end{array}ight], \quad\left[\begin{array}{l}
x_{1}(0) \\
x_{2}(0) \\
x_{3}(0)
\end{array}ight]=\left[\begin{array}{l}
1 \\
0 \\
0
\end{array}ight], \quad r(t)=2 u(t)
\]