Consider the following two linear systems $(x^{}=Ax+Bu,y=Cx)$

$A_1=\left[\begin{array}{ccc}0& 1& -3\end{array}\right]$

$-2$;$B_1=\left[\begin{array}{c}0\end{array}\right]$

$1,C_1=\left[\begin{array}{cc}2& 0\end{array}\right]$

$A_2=\left[\begin{array}{ccccccc}0& 1& 0& 0& 1& -11& -6\end{array}\right]$

$-6$

$0,B_2=\left[\begin{array}{c}0\end{array}\right]$

$0$

$1,C_2=\left[\begin{array}{ccc}6& 2& 0\end{array}\right]$

$($a$)$ Show that both systems system have the same transfer function $G(s)=\frac{Y(s)}{U(s)}($For the $3$rd order system, cancel out one oder of $s$ in the zero with one of the poles$)$

$($b$)$ Evaluate the controllability and observability for both systems