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

---

Definitions:

Months

Units of time, typically used to measure periods within a year, consisting of 28 to 31 days.

Invested

Assigning monetary assets with the prospect of gaining returns or profit.

Investment Value

The worth of an asset or security based on its potential to generate income, appreciation, or other benefits to an investor.

December

The twelfth and final month of the year in the Gregorian calendar.