$(10$ pts$)$ A system is shown below.

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

$x_2^{}=\left[\begin{array}{ccc}0& 1& -2\end{array}\right]$

$-3\left[\begin{array}{c}{x}_1\end{array}\right]$

$x_2+\left[\begin{array}{c}2\end{array}\right]$

$1u$

$y=\left[\begin{array}{cc}1& 0\end{array}\right]\left[\begin{array}{c}{x}_1\end{array}\right]$

$x_2$

a$)$ Obtain the transfer function of the system $Y\frac{S}{U}(S).$

b$)$ Is the system controllable? Show your work.