Consider the following system:

$x_1^{}(t)=-5x_1(t)-3x_2(t)+\frac{1}{2}u(t)$

$x_2^{}(t)=2x_1(t)$

$y(t)=3x_2(t)$

i$)$ Compute the $A,B,C,D$ matrices to put this set of equations into standard State Space form, and hence compute the transfer function $G(s)=\frac{Y(s)}{U(s)}.$

ii$)$ Compute the impulse response $g(t)$ of this system.

iii$)$ Compute the step response $s(t)$ of this system.

iv$)$ Suppose I applied a change of State Space Coordinates, $x=Tz($for $T$ nonsingular$).$ Which of the above quantities $(A,B,C,D,G(s),g(t),s(t))$ would change $($explain$)?$