A state variable system \(\dot{x}(t)=\left[\begin{array}{rr}0 & 1 \\ 0 & -3\end{array}ight] x(t)+\left[\begin{array}{l}1 \\ 0\end{array}ight] u(t)\), with the initial condition \(x(0)=\left[\begin{array}{ll}-1 & 3\end{array}ight]^{\mathrm{T}}\) and the unit step input \(u(t)\) has.

The state transition matrix
(a) \(\left[\begin{array}{cc}1 & \frac{1}{3}\left(1-e^{-3 t}ight) \\ 0 & e^{-3 t}\end{array}ight]\)
(b) \(\left[\begin{array}{cc}1 & \frac{1}{3}\left(e^{-t}-e^{-3 t}ight) \\ 0 & e^{-t}\end{array}ight]\)
(c) \(\left[\begin{array}{cc}1 & \frac{1}{3}\left(e^{-t}-e^{-3 t}ight) \\ 0 & e^{-3 t}\end{array}ight]\)
(d) \(\left[\begin{array}{cc}1 & \left(1-e^{-t}ight) \\ 0 & e^{-t}\end{array}ight]\).