The Solution of the System $\mathbf { X } ^ { \prime } = \left( \begin{array} { l l } 1 & - 3 \\2 & - 4\end{array} \right) \mathbf { X }$

Multiple Choice

The solution of the system $\mathbf { X } ^ { \prime } = \left( \begin{array} { l l } 1 & - 3 \\2 & - 4\end{array} \right) \mathbf { X }$ is

A) $\mathbf { X } = c _ { 1 } \left( \begin{array} { l } 3 \\2\end{array} \right) e ^ { - t } + c _ { 2 } \left( \begin{array} { l } 1 \\1\end{array} \right) e ^ { - 2 t }$
B) $\mathbf { X } = c _ { 1 } \left( \begin{array} { l } 3 \\2\end{array} \right) e ^ { t } + c _ { 2 } \left( \begin{array} { l } 1 \\1\end{array} \right) e ^ { 2 t }$
C) $\mathbf { X } = c _ { 1 } \left( \begin{array} { l } 2 \\3\end{array} \right) e ^ { - t } + c _ { 2 } \left( \begin{array} { l } 1 \\1\end{array} \right) e ^ { - 2 t }$
D) $\mathbf { X } = c _ { 1 } \left( \begin{array} { l } 2 \\3\end{array} \right) e ^ { t } + c _ { 2 } \left( \begin{array} { l } 1 \\1\end{array} \right) e ^ { 2 t }$
E) none of the above