A system is described by the state equation

\[
\left[\begin{array}{l}
\dot{x}_{1} \\
\dot{x}_{2}
\end{array}ight]=\left[\begin{array}{ll}
2 & 0 \\
0 & 2
\end{array}ight]\left[\begin{array}{l}
x_{1} \\
x_{2}
\end{array}ight]+\left[\begin{array}{l}
1 \\
1
\end{array}ight] u
\]

The state transition matrix of the system is
(a) \(\left[\begin{array}{cc}e^{2 t} & 0 \\ 0 & e^{2 t}\end{array}ight]\)
(b) \(\left[\begin{array}{cc}e^{-2 t} & 0 \\ 0 & e^{-2 t}\end{array}ight]\)
(c) \(\left[\begin{array}{cc}e^{2 t} & 1 \\ 1 & e^{2 t}\end{array}ight]\)
(d) \(\left[\begin{array}{cc}e^{-2 t} & 1 \\ 1 & e^{-2 t}\end{array}ight]\).