Consider a linear system whose state space representation is x and (t) = Ax (t). If the initial state vector of the system is x (0) =$ \left[ \begin{array} \ 1 \\ -2 \end{array} \right] $, the system response is x (t) = $ \left( \begin{array} \ e^{-2t} \\ -2 e^{-2t} \end{array} \right) $. If the initial state vector of the system changes, the system response becomes x(t) = $ \left[ \begin{array} \ e^{-t} \\ -e^{-6} \end{array} \right] $.

The system matrix A is