The Solution of the System $X ^ { \prime } = \left( \begin{array} { c c } - 3 & - 1 \\1 & - 1\end{array} \right) X$

question 14

Multiple Choice

The solution of the system $X ^ { \prime } = \left( \begin{array} { c c } - 3 & - 1 \\1 & - 1\end{array} \right) X$ is

• A) \(\mathbf { X } = c _ { 1 } \left( \begin{array} { c }
• - 1 \\
• 1
• \end{array} \right) e ^ { - 2 t } + c _ { 2 } \left[ \left( \begin{array} { c }
• - 1 \\
• 1
• \end{array} \right) t e ^ { - 2 t } + \left( \begin{array} { l }
• 1 \\
• 0
• \end{array} \right) e ^ { - 2 t } \right]\)
• B) \(\mathbf { X } = c _ { 1 } \left( \begin{array} { c }
• - 1 \\
• 1
• \end{array} \right) e ^ { - 2 t } + c _ { 2 } \left( \begin{array} { c }
• - 1 \\
• 1
• \end{array} \right) t e ^ { - 2 t } + c _ { 3 } \left( \begin{array} { l }
• 1 \\
• 0
• \end{array} \right) e ^ { - 2 t }\)
• C) \(X = c _ { 1 } \left( \begin{array} { c }
• - 1 \\
• 1
• \end{array} \right) e ^ { - 2 t } + c _ { 2 } \left( \begin{array} { c }
• 1 \\
• - 1
• \end{array} \right) t e ^ { - 2 t }\)
• D) \(X = c _ { 1 } \left( \begin{array} { c }
• - 1 \\
• 1
• \end{array} \right) e ^ { - 2 t } + c _ { 2 } \left( \begin{array} { l }
• 1 \\
• 2
• \end{array} \right) e ^ { - t }\)
• E) none of the above

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