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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Definitions:

Central Nervous System

The part of the nervous system comprising the brain and spinal cord, responsible for processing and transmitting information.

Meninges

Protective membranes that cover the brain and spinal cord, comprising the dura mater, arachnoid mater, and pia mater.

Spinal Cord

In vertebrates, the nerve cord that is continuous with the base of the brain and housed within the vertebral column.

Medulla Oblongata

In vertebrates, part of the brain stem that is continuous with the spinal cord; controls heartbeat, blood pressure, breathing, and other vital functions.