The Solution Of $$\mathbf { X } ^ { \prime } = \left( \begin{array} { c c } 1 & - 2 \\1 & 4\end{array} \right) \mathbf { X }$$

Multiple Choice

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

A) $$X = c _ { 1 } \left( \begin{array} { l } 2 \\1\end{array} \right) e ^ { - 2 t } + c _ { 2 } \left( \begin{array} { l } 1 \\1\end{array} \right) e ^ { - 3 t }$$
B) $$X = c _ { 1 } \left( \begin{array} { l } 2 \\1\end{array} \right) e ^ { - 2 t } + c _ { 2 } \left( \begin{array} { c } 1 \\- 1\end{array} \right) e ^ { - 3 t }$$
C) $$X = c _ { 1 } \left( \begin{array} { c } - 2 \\- 1\end{array} \right) e ^ { 2 t } + c _ { 2 } \left( \begin{array} { c } 1 \\- 1\end{array} \right) e ^ { 3 t }$$
D) $$X = c _ { 1 } \left( \begin{array} { c } 2 \\- 1\end{array} \right) e ^ { 2 t } + c _ { 2 } \left( \begin{array} { c } 1 \\- 1\end{array} \right) e ^ { 3 t }$$
E) $$X = c _ { 1 } \left( \begin{array} { c } 1 \\- 2\end{array} \right) e ^ { 2 t } + c _ { 2 } \left( \begin{array} { c } 1 \\- 1\end{array} \right) e ^ { 3 t }$$