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

question 11

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) \[\mathbf { X } = c _ { 1 } \left[ \left( \begin{array} { l }
• 1 \\
• 1
• \end{array} \right) \cos ( 2 t ) - \left( \begin{array} { c }
• 0 \\
• - 1
• \end{array} \right) \sin ( 2 t ) \right] + c _ { 2 } \left[ \left( \begin{array} { l }
• 1 \\
• 1
• \end{array} \right) \sin ( 2 t ) + \left( \begin{array} { c }
• 0 \\
• - 1
• \end{array} \right) \cos ( 2 t ) \right]\]

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