The Solution Of $$\mathbf { X } ^ { \prime } = \left( \begin{array} { c c } 1 & - 2 \\1 & 4\end{array} \right) \mathbf { X }$$

question 13

Multiple Choice

The solution of $$\mathbf { X } ^ { \prime } = \left( \begin{array} { c c } 1 & - 2 \\1 & 4\end{array} \right) \mathbf { X }$$ is

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

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Definitions:

Period Costs

Expenses that are not directly tied to the production of goods, such as sales and marketing expenses, which are expensed in the period they are incurred.

Factory Building Utilities

Expenses related to utilities within a factory building, including costs for electricity, gas, water, and sewage.

Direct Costs

Costs directly associated with the manufacturing of specific products or services, including labor and raw materials.

Indirect Costs

Expenses not directly tied to a specific project, product, or activity, such as administrative salaries and facility maintenance.