Solve the System Using the Inverse That Is Given for the Coefficient

question 141

Multiple Choice

Solve the system using the inverse that is given for the coefficient matrix.
- $x + 2 y + 3 z = 6$ $x + y + z = - 8$ $x \quad - 2 z = 12$ The inverse of $\left[ \begin{array} { l l l } 1 & 2 & 3 \\ 1 & 1 & 1 \\ 1 & 0 & - 2 \end{array} \right]$ is $\left[ \begin{array} { r r r } - 2 & 4 & - 1 \\ 3 & - 5 & 2 \\ - 1 & 2 & - 1 \end{array} \right]$ .

• A) \(\{ ( - 56,82 , - 34 ) \}\)
• B) \(\{ ( - 48,88 , - 34 ) \}\)
• C) \(\{ ( 6,0,0 ) \}\)
• D) \(\{ ( - 8,2,2 ) \}\)

---

Definitions:

Constant Returns

A situation in which the rate of increase in output is directly proportional to the increase in inputs in the production process.

Scale

The size or level of operation, indicating the scope or extent of something, often used in discussions of production or economic activities.

Production Function

An economic model that describes how output is created by varying inputs of production like labor and capital.

Technological Knowledge

Society’s understanding of the best ways to produce goods and services.