Question $7$: Consider the following state space system

$x^{}=Fx+Gu$

$y=Hx+Ju$

with

$F=\left[\begin{array}{cc}-2& 0\\ 5& 3\end{array}\right],G=\left[\begin{array}{c}0\\ 1\end{array}\right],H=\left[\begin{array}{cc}1& 0\end{array}\right],J=0$

a$)$ Can you place the poles of this system to $-2$ and $-10.$ Why?

b$)$ Can you place the poles of this system to $-3$ and $-8.$ Why?

Question $8$: Consider the following state space system

$x^{}=Fx+Gu$

$y=Hx+Ju$

with

$F=\left[\begin{array}{cc}-5& 0\\ 7& 2\end{array}\right],G=\left[\begin{array}{c}0\\ 1\end{array}\right],H=\left[\begin{array}{cc}1& 0\end{array}\right],J=0$

a$)$ Can you place the poles of this system to $-5$ and $-5.$ Why?

b$)$ Can you place the poles of this system to $-1$ and $-1.$ Why?