The systems together with inputs and initial conditions are given below. Determine system response in each.

(a) \(\quad \dot{x}=-2 x+3 r(t)\)

\[
y=4 x
\]

\[
\begin{aligned}
x(0) & =10 \\
r(t) & =5 u(t)
\end{aligned}
\]

(b) \(\left[\begin{array}{l}\dot{x}_{1} \\ \dot{x}_{2}\end{array}ight]=\left[\begin{array}{rr}0 & 1 \\ -6 & -8\end{array}ight]\left[\begin{array}{l}x_{1} \\ x_{2}\end{array}ight]+\left[\begin{array}{l}1 \\ 1\end{array}ight] r\)

\[
y=\left[\begin{array}{ll}
1 & -1
\end{array}ight]\left[\begin{array}{l}
x_{1} \\
x_{2}
\end{array}ight]
\]

\[
\begin{aligned}
{\left[\begin{array}{l}
x_{1}(0) \\
x_{2}(0)
\end{array}ight] } & =\left[\begin{array}{r}
7 \\
-3
\end{array}ight] \\
r(t) & =\delta(t) ; \text { the unit impulse function. }
\end{aligned}
\]