The Solution Of $$X ^ { \prime } = \left( \begin{array} { c c c } 4 & 0 & 0 \\0 & 3 & 1 \\0 & - 1 & 1\end{array} \right) X$$

question 42

Multiple Choice

The solution of $$X ^ { \prime } = \left( \begin{array} { c c c } 4 & 0 & 0 \\0 & 3 & 1 \\0 & - 1 & 1\end{array} \right) X$$ are

• A) \[X = c _ { 1 } \left( \begin{array} { l }
• 0 \\
• 1 \\
• 0
• \end{array} \right) e ^ { 4 t } + c _ { 2 } \left( \begin{array} { c }
• 0 \\
• 1 \\
• - 1
• \end{array} \right) e ^ { 2 t } + c _ { 3 } \left[ \left( \begin{array} { c }
• 0 \\
• 1 \\
• - 1
• \end{array} \right) t e ^ { 2 t } + \left( \begin{array} { l }
• 0 \\
• 1 \\
• 0
• \end{array} \right) e ^ { 2 t } \right]\]
• B) \[X = c _ { 1 } \left( \begin{array} { c }
• 0 \\
• 1 \\
• - 1
• \end{array} \right) e ^ { 4 t } + c _ { 2 } \left( \begin{array} { l }
• 0 \\
• 1 \\
• 0
• \end{array} \right) e ^ { 2 t } + c _ { 3 } \left[ \left( \begin{array} { l }
• 0 \\
• 1 \\
• 0
• \end{array} \right) t e ^ { 2 t } + \left( \begin{array} { l }
• 0 \\
• 1 \\
• 0
• \end{array} \right) e ^ { 2 t } \right]\]
• C) \[X = c _ { 1 } \left( \begin{array} { l }
• 1 \\
• 0 \\
• 0
• \end{array} \right) e ^ { 4 t } + c _ { 2 } \left( \begin{array} { c }
• 0 \\
• 1 \\
• - 1
• \end{array} \right) e ^ { 2 t } + c _ { 3 } \left[ \left( \begin{array} { c }
• 0 \\
• 1 \\
• - 1
• \end{array} \right) t e ^ { 2 t } + \left( \begin{array} { l }
• 0 \\
• 1 \\
• 0
• \end{array} \right) e ^ { 2 t } \right]\]
• D) \[X = c _ { 1 } \left( \begin{array} { l }
• 1 \\
• 0 \\
• 0
• \end{array} \right) e ^ { 4 t } + c _ { 2 } \left( \begin{array} { l }
• 0 \\
• 1 \\
• 1
• \end{array} \right) e ^ { 2 t } + c _ { 3 } \left[ \left( \begin{array} { l }
• 0 \\
• 1 \\
• 1
• \end{array} \right) t e ^ { 2 t } + \left( \begin{array} { l }
• 0 \\
• 1 \\
• 0
• \end{array} \right) e ^ { 2 t } \right]\]
• E) \[X = c _ { 1 } \left( \begin{array} { l }
• 1 \\
• 0 \\
• 0
• \end{array} \right) e ^ { 4 t } + c _ { 2 } \left( \begin{array} { c }
• 1 \\
• - 1 \\
• 0
• \end{array} \right) e ^ { 2 t } + c _ { 3 } \left[ \left( \begin{array} { c }
• 1 \\
• - 1 \\
• 0
• \end{array} \right) t e ^ { 2 t } + \left( \begin{array} { l }
• 0 \\
• 1 \\
• 0
• \end{array} \right) e ^ { 2 t } \right]\]

---

Definitions:

Success-Stimulus

The motivation or drive that individuals or organizations experience following successful outcomes, encouraging further efforts or achievements.

Exchange Network

A social structure formed around the dynamics of exchanging goods, services, or information among individuals or organizations.

Valued Resources

Assets, commodities, or services that are highly regarded or deemed beneficial by individuals or societies.

Emerson

Ralph Waldo Emerson was a leading figure in the transcendentalist movement of the mid-19th century, known for his work as an American essayist, lecturer, philosopher, and poet.