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

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

A) $\mathbf { X } = c _ { 1 } \left( \begin{array} { c } 1 \\- 1\end{array} \right) e ^ { - t } + c _ { 2 } \left[ \left( \begin{array} { c } 1 \\- 1\end{array} \right) t e ^ { - t } + \left( \begin{array} { c } - 1 / 2 \\0\end{array} \right) e ^ { - t } \right]$
B) $\mathbf { X } = c _ { 1 } \left( \begin{array} { c } 1 \\- 1\end{array} \right) e ^ { t } + c _ { 2 } \left[ \left( \begin{array} { c } 1 \\- 1\end{array} \right) t e ^ { t } + \left( \begin{array} { c } - 1 / 2 \\0\end{array} \right) e ^ { t } \right]$
C) $X = c _ { 1 } \left( \begin{array} { c } 1 \\- 1\end{array} \right) e ^ { - t } + c _ { 2 } \left( \begin{array} { c } - 1 \\1\end{array} \right) e ^ { t }$
D) $\mathbf { X } = c _ { 1 } \left( \begin{array} { c } 1 \\- 1\end{array} \right) e ^ { - t } + c _ { 2 } \left( \begin{array} { l } 1 \\2\end{array} \right) e ^ { t }$
E) none of the above

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