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

question 22

Multiple Choice

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

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

Recognize and adapt to various instructional styles.

Enhance preparation for courses and lectures.

Improve listening and comprehension skills in a learning environment.

Identify and implement strategies for retaining information and knowledge.

---

Definitions:

Recursive Algorithms

Procedures or methods where the solution to a problem depends on solutions to smaller instances of the same problem.

While Loops

A statement in programming that enables the repeated execution of code as long as a specified Boolean condition remains true.

Limiting Condition

A constraint or restriction defined in a program or system that limits its execution or functionality.

ExampleRecursion

ExampleRecursion typically refers to a demonstration or example that illustrates how recursion works, which is a method where the solution to a problem depends on solutions to smaller instances of the same problem.