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

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Definitions:

T-statistic

A statistic used in hypothesis testing, specifically to determine the significance of the difference between two sample means.

Hypothesized Population Mean

The expected value of the mean for a population, as proposed in a hypothesis, that is tested for accuracy against sample data.

T-statistic

A ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error, used in hypothesis testing.

Sample Mean

The average value of all observations in a sample.