$6$ Controllability

$($a$)$ Why do we need to check if a system is controllable before doing pole placement?

$($b$)$ Determine if the following system is controllable:

$\left[\begin{array}{c}{x}_1^{}\\ x_2^{}\\ y\end{array}\right]=\left[\begin{array}{ccc}1& 1& 1\\ 0& 2& 0\\ 1& 0& 0\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ u\end{array}\right]$

$($c$)$ Determine if the following system is controllable:

$\left[\begin{array}{c}{x}_1^{}\\ x_2^{}\\ y\end{array}\right]=\left[\begin{array}{cccc}0& 1& 1& 0\\ -2& -3& 0& 1\\ 1& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ u_1\\ u_2\end{array}\right]$