The Solution of the System $\mathbf { X } ^ { \prime } = \left( \begin{array} { l l } 1 & - 3 \\2 & - 4\end{array} \right) \mathbf { X }$

question 40

Multiple Choice

The solution of the system $\mathbf { X } ^ { \prime } = \left( \begin{array} { l l } 1 & - 3 \\2 & - 4\end{array} \right) \mathbf { X }$ is

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

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