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 equation
(a) \(x(t)=\left[\begin{array}{c}t-e^{-t} \\ e^{-t}\end{array}ight]\)
(b) \(x(t)=\left[\begin{array}{c}t-e^{-t} \\ 3 e^{-3 t}\end{array}ight]\)
(c) \(x(t)=\left[\begin{array}{c}t-e^{-3 t} \\ 3 e^{-3 t}\end{array}ight]\)
(d) \(x(t)=\left[\begin{array}{c}t-e^{-3 t} \\ e^{-t}\end{array}ight]\)