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

question 11

Multiple Choice

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

• A) \[\mathbf { X } = c _ { 1 } \left[ \left( \begin{array} { c }
• 1 \\
• - 1
• \end{array} \right) \cos t - \left( \begin{array} { l }
• 0 \\
• 1
• \end{array} \right) \sin t \right] + c _ { 2 } \left[ \left( \begin{array} { c }
• 1 \\
• - 1
• \end{array} \right) \sin t + \left( \begin{array} { l }
• 0 \\
• 1
• \end{array} \right) \cos t \right]\]
• B) \[X = c _ { 1 } \left( \begin{array} { l }
• 1 \\
• 0
• \end{array} \right) e ^ { \sqrt { 3 } t } + c _ { 2 } \left( \begin{array} { l }
• 0 \\
• 1
• \end{array} \right) e ^ { - \sqrt { 3 } t }\]
• C) \[\mathbf { X } = c _ { 1 } \left( \begin{array} { l }
• 1 \\
• 0
• \end{array} \right) e ^ { t } + c _ { 2 } \left( \begin{array} { l }
• 0 \\
• 1
• \end{array} \right) e ^ { - t }\]
• D) \[\begin{array} { l }
• X = c _ { 1 } \left[ \left( \begin{array} { c }
• 1 \\
• - 1
• \end{array} \right) \cos ( \sqrt { 3 } t ) - \left( \begin{array} { l }
• 0 \\
• 1
• \end{array} \right) \sin ( \sqrt { 3 } t ) \right] + \\
• c _ { 2 } \left[ \left( \begin{array} { c }
• 1 \\
• - 1
• \end{array} \right) \sin ( \sqrt { 3 } t ) + \left( \begin{array} { l }
• 0 \\
• 1
• \end{array} \right) \cos ( \sqrt { 3 } t ) \right]
• \end{array}\]
• E) \[\mathbf { X } = c _ { 1 } \left[ \left( \begin{array} { l }
• 1 \\
• 1
• \end{array} \right) \cos ( 2 t ) - \left( \begin{array} { c }
• 0 \\
• - 1
• \end{array} \right) \sin ( 2 t ) \right] + c _ { 2 } \left[ \left( \begin{array} { l }
• 1 \\
• 1
• \end{array} \right) \sin ( 2 t ) + \left( \begin{array} { c }
• 0 \\
• - 1
• \end{array} \right) \cos ( 2 t ) \right]\]

---

Definitions:

Overhead

Indirect costs related to manufacturing or business operations that do not directly tie to a specific product or activity, such as utilities, rent, and management salaries.

Equivalent Units

A concept in cost accounting used to allocate costs to partially completed goods, measured in terms of the amount of work done on them.

Materials

Items or substances from which something is made or can be made, often used in the context of production or manufacturing.

FIFO Method

The First-In, First-Out (FIFO) method is an inventory valuation strategy where the oldest inventory items are recorded as sold first.