i need some help. I have this kind of system
$\dot{x} = Ax(t) + Bu(t)$
$y(t) = Cx(t)$
$x(0) = 0$
$A = \begin{bmatrix} 2 && -1 \\ 2 && -5\end{bmatrix}$ $B =\begin{bmatrix} 2 && 2 \end{bmatrix}$ $C =\begin{bmatrix} 0 \\1 \end{bmatrix}$
Now i need to get Transfer function (https://en.wikipedia.org/wiki/Transfer_function). So the formula is : $G(s)=\frac{Y(s)}{U(s)}.$ and i dont know how go do this. Anybody can help?
Edit: i found on the internet this formula : $G(s) = C(sI - A)^{-1}B$
The $(sI - A)^{-1}$ i did by using formula $M^{-1} = (M^{D})^{T} * \frac{1}{detM}$
I got something like this : $G(s) = \begin{bmatrix} \frac{2s}{s^{2} + 3s - 8} \\ \frac{2s+8}{s^{2} + 3s - 8} \end{bmatrix}$ The question is: is it correct?