A system modelled as

\[
\dot{x}(t)=\mathrm{A} x(t)
\]

generates state response \(x(t)=\left[\begin{array}{c}e^{-2 t} \\ -2 e^{-2 t}\end{array}ight]\) for initial vector \(x(0)=\left[\begin{array}{c}1 \\ -2\end{array}ight]\) and \(x(t)=\left[\begin{array}{c}e^{-t} \\ -e^{-t}\end{array}ight]\) for \(x(0)=\left[\begin{array}{r}1 \\ -1\end{array}ight]\). Find the system matrix A and state transition matrix (STM).