The Solution of the System $\mathbf { X } ^ { \prime } = \left( \begin{array} { l l } 2 & 2 \\1 & 1\end{array} \right) \mathbf { X }$

question 19

Multiple Choice

The solution of the system $\mathbf { X } ^ { \prime } = \left( \begin{array} { l l } 2 & 2 \\1 & 1\end{array} \right) \mathbf { X }$ is

• A) \(X = c _ { 1 } \left( \begin{array} { c }
• - 1 \\
• 1
• \end{array} \right) e ^ { - t } + c _ { 2 } \left( \begin{array} { l }
• 2 \\
• 1
• \end{array} \right) e ^ { - 3 t }\)
• B) \(\mathbf { X } = c _ { 1 } \left( \begin{array} { c }
• - 1 \\
• 1
• \end{array} \right) e ^ { t } + c _ { 2 } \left( \begin{array} { l }
• 2 \\
• 1
• \end{array} \right) e ^ { 3 t }\)
• C) \(X = c _ { 1 } \left( \begin{array} { c }
• - 1 \\
• 1
• \end{array} \right) e ^ { - t } + c _ { 2 } \left( \begin{array} { l }
• 1 \\
• 2
• \end{array} \right) e ^ { - 3 t }\)
• D) \(\mathbf { X } = c _ { 1 } \left( \begin{array} { c }
• - 1 \\
• 1
• \end{array} \right) e ^ { t } + c _ { 2 } \left( \begin{array} { l }
• 1 \\
• 2
• \end{array} \right) e ^ { 3 t }\)
• E) none of the above

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Definitions:

Direct Labor Cost

The compensation given to employees who are directly engaged in manufacturing goods or providing services.

Direct Materials Cost

Direct Materials Cost is the expenditure for raw materials that are directly traceable to the production of a specific product or service.

Payment of Dividends

The distribution of a portion of a company's earnings to its shareholders as determined by the company's board of directors.

Factory Overhead

Indirect costs related to manufacturing, such as utilities, maintenance, and salaries of supervisory personnel not directly involved in production.