The Solution Of $\mathbf { X } ^ { \prime } = \left( \begin{array} { c c } 1 & - 2 \\1 & 4\end{array} \right) \mathbf { X }$

question 19

Multiple Choice

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

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

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Definitions:

Group Polarization

Group polarization occurs when the attitude of a group becomes more extreme than the initial inclination of its members after group discussions.

Group Polarization

The effect where the dominant opinions or convictions of a group intensify or become more radical after discussions among its members.

Deindividuation

A psychological state where an individual loses self-awareness and a sense of individuality, often in group contexts, leading to uninhibited behavior.

Social Facilitation

The tendency for people to perform differently when in the presence of others, usually improving on simple tasks and doing poorly on complex tasks.