Determine the state$-$space model of the system given by the following transfer function:

$\frac{Y(s)}{U(s)}=\frac{6}{3s^2-12s+15}$

Select one:

a$.\left[\begin{array}{c}{x}_1^{}\\ x_2^{}\end{array}\right]=\left[\begin{array}{cc}0& 1\\ -5& 4\end{array}\right]*\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}0\\ 6\end{array}\right]*u$

$y=\left[\begin{array}{cc}1& 0\end{array}\right]*\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+[0]*u$

b$.\left[\begin{array}{c}{x}_1^{}\\ x_2^{}\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 5& -4\end{array}\right]*\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}0\\ 2\end{array}\right]*u$

$y=\left[\begin{array}{cc}1& 0\end{array}\right]*\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+[0]*u$

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

$x_2^{}=\left[\begin{array}{ccc}0& 1& -4\end{array}\right]$

$5*\left[\begin{array}{c}{x}_1\end{array}\right]$

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

$6*u$

$y=\left[\begin{array}{cc}1& 0\end{array}\right]*\left[\begin{array}{c}{x}_1\end{array}\right]$

$x_2+[0]*u$

d$.$ None of these

e$.\left[\begin{array}{c}{x}_1^{}\\ x_2^{}\end{array}\right]=\left[\begin{array}{cc}0& 1\\ -5& 4\end{array}\right]*\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}0\\ 2\end{array}\right]*uy=\left[\begin{array}{cc}0& 1\end{array}\right]*\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+[0]*u$