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

Multiple Choice

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

A) $$\mathbf { X } = c _ { 1 } \left[ \left( \begin{array} { c } 1 \\- 1\end{array} \right) \cos t - \left( \begin{array} { l } 0 \\1\end{array} \right) \sin t \right] + c _ { 2 } \left[ \left( \begin{array} { c } 1 \\- 1\end{array} \right) \sin t + \left( \begin{array} { l } 0 \\1\end{array} \right) \cos t \right]$$
B) $$X = c _ { 1 } \left( \begin{array} { l } 1 \\0\end{array} \right) e ^ { \sqrt { 3 } t } + c _ { 2 } \left( \begin{array} { l } 0 \\1\end{array} \right) e ^ { - \sqrt { 3 } t }$$
C) $$\mathbf { X } = c _ { 1 } \left( \begin{array} { l } 1 \\0\end{array} \right) e ^ { t } + c _ { 2 } \left( \begin{array} { l } 0 \\1\end{array} \right) e ^ { - t }$$
D) $$\begin{array} { l } X = c _ { 1 } \left[ \left( \begin{array} { c } 1 \\- 1\end{array} \right) \cos ( \sqrt { 3 } t ) - \left( \begin{array} { l } 0 \\1\end{array} \right) \sin ( \sqrt { 3 } t ) \right] + \\c _ { 2 } \left[ \left( \begin{array} { c } 1 \\- 1\end{array} \right) \sin ( \sqrt { 3 } t ) + \left( \begin{array} { l } 0 \\1\end{array} \right) \cos ( \sqrt { 3 } t ) \right]\end{array}$$
E) $$\mathbf { X } = c _ { 1 } \left[ \left( \begin{array} { l } 1 \\1\end{array} \right) \cos ( 2 t ) - \left( \begin{array} { c } 0 \\- 1\end{array} \right) \sin ( 2 t ) \right] + c _ { 2 } \left[ \left( \begin{array} { l } 1 \\1\end{array} \right) \sin ( 2 t ) + \left( \begin{array} { c } 0 \\- 1\end{array} \right) \cos ( 2 t ) \right]$$