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:

Cash Outflows

Money spent or costs incurred by a business or individual, resulting in a decrease in cash assets.

Internal Rate

Internal rate usually refers to the internal rate of return (IRR), a financial metric used to assess the profitability of investments by calculating the interest rate that makes the net present value (NPV) of all cash flows from a particular project or investment equal to zero.

Accept

In financial terms, it often refers to a bank's agreement to honor a draft or other financial instrument payable at a future date.

Net Present Value

The difference between the present value of cash inflows and outflows over a period of time, used in capital budgeting to assess profitability of investments.