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

question 26

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

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