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

---

Definitions:

Positive Correlation

A relationship between two variables in which both variables move in the same direction, indicating that as one variable increases, the other also increases.

Alcohol Consumption

The act of drinking beverages containing ethanol, which can have various effects on health and behavior depending on the amount and frequency of intake.

Negative Correlation

A connection between two variables where one variable rises while the other falls.

Incidence of Dental Disease

Refers to the frequency or rate at which new cases of dental diseases occur in a population over a specified period of time.