Question $1$:

Let us consider the following state$-$space equations:

$\left[\begin{array}{c}{x}_1^{}\end{array}\right]$

$x_2^{}=\left[\begin{array}{ccc}0& 1& -5\end{array}\right]$

$-6\left[\begin{array}{c}{x}_1\end{array}\right]$

$x_2+\left[\begin{array}{c}0\end{array}\right]$

$1u(t)$

$y=\left[\begin{array}{cc}8& 1\end{array}\right]\left[\begin{array}{c}{x}_1\end{array}\right]$

$x_2$

Demonstrate that the Transfer Function is :

$G(s)=\frac{s+8}{s^2+5s+6}$