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:

Pustule

A small blister or pimple on the skin containing pus.

Turgor

The state of being turgid or swollen, usually referring to the skin's elasticity and how it indicates hydration and health.

Abrasion

A wound caused by superficial damage to the skin, usually due to scraping or friction.

-ion

A suffix typically used in science denoting an action or process or a condition or state.