MATLAB Problems

$7\mathrm{.}16$ Given the SSR

$x^{}=\left[\begin{array}{cc}-0\mathrm{.}2& -0\mathrm{.}6\\ 2& -4\end{array}\right]x+\left[\begin{array}{c}0\\ 1\mathrm{.}5\end{array}\right]u,y=\left[\begin{array}{cc}1& 0\end{array}\right]x$

a$.$ Compute the eigenvalues $"$by hand."

b$.$ Use MATLAB to verify your answer in part $($a$).$

c$.$ Describe the free response of the output $y(t)$ given an arbitrary initial state $x(0).$

d$.$ Use MATLAB or Simulink to verify your answer in part $($c$).$ The initial state vector is $x(0)={\left[\begin{array}{cc}{x}_1(0)& x_2(0)\end{array}\right]}^T={\left[\begin{array}{cc}-2& -1\end{array}\right]}^T$