The Solution Of $$\mathbf { X } ^ { \prime } = \left( \begin{array} { l l } 1 & - 2 \\1 & - 1\end{array} \right) \mathbf { X }$$

question 25

Multiple Choice

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

• A) \[\mathbf { X } = c _ { 1 } \left[ \left( \begin{array} { l }
• 2 \\
• 1
• \end{array} \right) \cos t - \left( \begin{array} { c }
• 0 \\
• - 1
• \end{array} \right) \sin t \right] + c _ { 2 } \left[ \left( \begin{array} { l }
• 2 \\
• 1
• \end{array} \right) \sin t + \left( \begin{array} { c }
• 0 \\
• - 1
• \end{array} \right) \cos t \right]\]
• B) \[X = c _ { 1 } \left( \begin{array} { l }
• 1 \\
• 0
• \end{array} \right) e ^ { \sqrt { 3 } t } + c _ { 2 } \left( \begin{array} { l }
• 0 \\
• 1
• \end{array} \right) e ^ { - \sqrt { 3 } t }\]
• C) \[\mathbf { X } = c _ { 1 } \left( \begin{array} { l }
• 1 \\
• 0
• \end{array} \right) e ^ { t } + c _ { 2 } \left( \begin{array} { l }
• 0 \\
• 1
• \end{array} \right) e ^ { - t }\]
• D) \[\begin{array} { l }
• \mathrm { X } = c _ { 1 } \left[ \left( \begin{array} { l }
• 2 \\
• 1
• \end{array} \right) \cos ( \sqrt { 3 } t ) - \left( \begin{array} { c }
• 0 \\
• - 1
• \end{array} \right) \sin ( \sqrt { 3 } t ) \right] + \\
• c _ { 2 } \left[ \left( \begin{array} { l }
• 2 \\
• 1
• \end{array} \right) \sin ( \sqrt { 3 } t ) + \left( \begin{array} { c }
• 0 \\
• - 1
• \end{array} \right) \cos ( \sqrt { 3 } t ) \right]
• \end{array}\]
• E) \[\mathbf { X } = c _ { 1 } \left[ \left( \begin{array} { l }
• 2 \\
• 1
• \end{array} \right) \cos ( 2 t ) - \left( \begin{array} { c }
• 0 \\
• - 1
• \end{array} \right) \sin ( 2 t ) \right] + c _ { 2 } \left[ \left( \begin{array} { l }
• 2 \\
• 1
• \end{array} \right) \sin ( 2 t ) + \left( \begin{array} { c }
• 0 \\
• - 1
• \end{array} \right) \cos ( 2 t ) \right]\]

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Definitions:

Entropy

A measure of disorder or randomness in a closed system, often used in physics and information theory.

Equivalence

The state of being equal in value, function, or meaning.

Psychic Value

The importance or significance that an individual attaches to objects, events, or relationships as per their emotional or unconscious investment.

Desires

Strong feelings of wanting or wishing for something to happen or be the case.