Consider the two dynamic systems

$S_1,S_2$

$x_1^{}=-x_1+u,x_2^{}=2x_2+x_3+w$

$,x_3^{}=x_2-2x_3+w$

$y=x_1,z=x_2+x_3$

where $inR$ is a parameter.

$S_1$ has state $x_1,$ control $u$ and output $y.$

$S_2$ has state $(x_2,x_3),$ control $w$ and output $z.$

$($a$)$ Write down the matrix form of the system equations of $S_1$ and $S_2$ and determine whether

each system is controllable, observable.