A system is described by state transition matrix \(\phi(t)=\left[\begin{array}{cc}e^{-t} & 0 \\ 0 & e^{-2 t}\end{array}ight]\) and has initial conditions \(\left[\begin{array}{l}x_{1}(0) \\ x_{2}(0)\end{array}ight]=\left[\begin{array}{l}1 \\ 2\end{array}ight]\). The state of system after 0.5 seconds will be
(a) \(\left[\begin{array}{c}0.6 \\ 0.74\end{array}ight]\)
(b) \(\left[\begin{array}{c}0.74 \\ 0.6\end{array}ight]\)
(c) \(\left[\begin{array}{l}0.6 \\ 1.2\end{array}ight]\)
(d) \(\left[\begin{array}{c}1.2 \\ 0.37\end{array}ight]\)