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

Multiple Choice

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

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