B$-9-14.$ Consider the system given by

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

$x_2^{}$

$x_3^{}=\left[\begin{array}{ccccccc}2& 0& 0& 2& 0& 3& 1\end{array}\right]$

$0$

$0\left[\begin{array}{c}{x}_1\end{array}\right]$

$x_2$

$x_3+\left[\begin{array}{cccc}0& 1& 0& 1\end{array}\right]$

$0$

$1\left[\begin{array}{c}{u}_1\end{array}\right]$

$u_2$

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

$y_2=\left[\begin{array}{ccccc}1& 0& 0& 1& 0\end{array}\right]$

$0\left[\begin{array}{c}{x}_1\end{array}\right]$

$x_2$

$x_3$

Is the system completely state controllable and completely observable? Is the system completely output controllable?