Find the Inverse of the Matrix $$\left[ \begin{array} { c c c } 2 & - 5 & 3 \\2 & - 4 & 8 \\4 & - 9 & 11\end{array} \right]$$

question 8

Multiple Choice

Find the inverse of the matrix.
- $$\left[ \begin{array} { c c c } 2 & - 5 & 3 \\2 & - 4 & 8 \\4 & - 9 & 11\end{array} \right]$$

• A) \(\left[ \begin{array} { l l l } 1 & 0 & 14 \\ 0 & 1 & 5 \\ 0 & 0 & 0 \end{array} \right]\)
• B) No inverse
• C) \(\left[ \begin{array} { c c c } 1 & 0 & 14 \\ 0 & 1 & 5 \\ 0 & - 1 & 0 \end{array} \right]\)
• D) \(\left[ \begin{array} { c c c } 2 & 2 & 4 \\ - 5 & - 4 & - 9 \\ 3 & 8 & 11 \end{array} \right]\)

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Definitions:

Total Product

The overall quantity of output that a firm produces, usually within a given period of time, based on the input of resources.

Marginal Product

The additional output that is produced by employing one more unit of a particular input, such as labor or capital.

Average Product

The output per unit of input, calculated by dividing total output by the total amount of input used.

Short-Run

A period during which at least one input, typically capital, is fixed, influencing the flexibility of businesses to adjust to market changes.