Find the Inverse, If It Exists, for the Matrix $$\left[ \begin{array} { r r r r } 4 & - 2 & 0 & 3 \\12 & - 4 & 0 & 6 \\6 & - 8 & 0 & 9 \\0 & 0 & - 6 & 0\end{array} \right]$$

question 195

Multiple Choice

Find the inverse, if it exists, for the matrix.
- $$\left[ \begin{array} { r r r r } 4 & - 2 & 0 & 3 \\12 & - 4 & 0 & 6 \\6 & - 8 & 0 & 9 \\0 & 0 & - 6 & 0\end{array} \right]$$

• A) The inverse does not exist.
• B)
• \[\left[ \begin{array} { r r r r }
• - \frac { 1 } { 2 } & 3 & 0 & 3 \\
• \frac { 1 } { 4 } & - \frac { 3 } { 4 } & 0 & - \frac { 5 } { 6 } \\
• 0 & - \frac { 1 } { 2 } & 0 & - \frac { 1 } { 3 } \\
• 0 & 0 & - \frac { 1 } { 6 } & 0
• \end{array} \right]\]
• C)
• \[\left[ \begin{array} { r r r r }
• - \frac { 1 } { 2 } & \frac { 1 } { 4 } & 0 & 0 \\
• 3 & - \frac { 3 } { 4 } & - \frac { 1 } { 2 } & 0 \\
• 0 & 0 & 0 & - \frac { 1 } { 6 } \\
• 3 & - \frac { 5 } { 6 } & - \frac { 1 } { 3 } & 0
• \end{array} \right]\]
• D)
• \[\left[ \begin{array} { c c c c }
• \frac { 1 } { 4 } & - \frac { 1 } { 2 } & 0 & \frac { 1 } { 3 } \\
• \frac { 1 } { 12 } & - \frac { 1 } { 4 } & 0 & \frac { 1 } { 6 } \\
• \frac { 1 } { 6 } & - \frac { 1 } { 8 } & 0 & \frac { 1 } { 9 } \\
• 0 & 0 & - \frac { 1 } { 6 } & 0
• \end{array} \right]\]

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Definitions:

FIFO

An inventory valuation method where the first items purchased or produced are the first ones sold, impacting the cost of goods sold and inventory valuation.

LIFO

Last In, First Out, an inventory valuation method where the most recently produced or acquired items are the first to be expensed.

Income Taxes

Taxes on individual or corporate income.

Inventory Costing Method

A system used to evaluate the value of inventory, including methods such as First-In, First-Out (FIFO), Last-In, First-Out (LIFO), and average cost.