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

question 35

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

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