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

Multiple Choice

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

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