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

question 30

Multiple Choice

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

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

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Definitions:

Magnitude

The size, extent, or importance of something.

Correlation Coefficient

A numerical indicator that shows the degree to which multiple variables co-vary.

Negative Life Events

Significant adverse events or situations that can lead to stress and have potentially lasting impacts on an individual's mental health.

Perceptions of Stress

How an individual views or interprets stress, which can significantly affect their psychological and physical response to it.