Q$1.$ Given the state$-$space equations.

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

$x_2^{}=\left[\begin{array}{ccc}1& 1& 3\end{array}\right]$

$-2\left[\begin{array}{c}{x}_1\end{array}\right]$

$x_2+\left[\begin{array}{c}0\end{array}\right]$

$1u$

$y=\left[\begin{array}{cc}2& 2\end{array}\right]\left[\begin{array}{c}{x}_1\end{array}\right]$

$x_2$

change the state variable to

$z_1=3x_1+2x_2$

$z_2=7x_1+5x_2$

and write new equations for the variables $z_1$ and $z_2.$