Write the Augmented Matrix for the System $$\left\{ \begin{aligned}4 x + 9 y + 2 z & = 30 \\- 2 x + 6 y + 2 z & = 0 \\9 x + 6 y + 5 z & = 38\end{aligned} \right.$$

question 4

Multiple Choice

Write the augmented matrix for the system.
- $$\left\{ \begin{aligned}4 x + 9 y + 2 z & = 30 \\- 2 x + 6 y + 2 z & = 0 \\9 x + 6 y + 5 z & = 38\end{aligned} \right.$$

• A) \(\left[ \begin{array} { r r | r } 4 & 9 & 2 \\ - 2 & 6 & 2 \\ 9 & 5 \end{array} \right]\)
• B) \(\left[ \begin{array} { r r r | r } 30 & 2 & 9 & 4 \\ 0 & 2 & 6 & - 2 \\ 38 & 5 & 6 & 9 \end{array} \right]\)
• C) \(\left[ \begin{array} { r r r | r } 4 & 9 & 2 & 30 \\ - 2 & 6 & 2 & 0 \\ 9 & 6 & 5 & 38 \end{array} \right]\)
• D) \(\left[ \begin{array} { r r r | r } 4 & - 2 & 9 & 30 \\ 9 & 6 & 6 & 0 \\ 2 & 2 & 5 & 38 \end{array} \right]\)

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Definitions:

Fixed Manufacturing Overhead

Indirect manufacturing costs that remain constant regardless of the level of production, such as factory rent and salaries of permanent staff.

Variable Manufacturing Overhead

Variable manufacturing overhead includes all production costs that change with the level of production output and are not direct materials or direct labor, such as utilities for the manufacturing facility.

Direct Labour

The wages paid to workers directly involved in the production of goods or services, considered a variable cost.

Direct Materials

Raw materials that can be directly attributed to the production of specific goods or services.