Find the Inverse, If It Exists, for the Matrix $$\left[ \begin{array} { r r r r } 6 & - 3 & 6 & - 4 \\6 & - 2 & - 4 & - 3 \\12 & - 5 & 2 & - 7 \\0 & - 6 & 12 & 0\end{array} \right]$$

question 121

Multiple Choice

Find the inverse, if it exists, for the matrix.
- $$\left[ \begin{array} { r r r r } 6 & - 3 & 6 & - 4 \\6 & - 2 & - 4 & - 3 \\12 & - 5 & 2 & - 7 \\0 & - 6 & 12 & 0\end{array} \right]$$

• A)
• \[\left[ \begin{array} { r r r r }
• \frac { 1 } { 6 } & - \frac { 1 } { 3 } & \frac { 1 } { 6 } & - \frac { 1 } { 4 } \\
• \frac { 1 } { 6 } & - \frac { 1 } { 2 } & - \frac { 1 } { 4 } & - \frac { 1 } { 3 } \\
• \frac { 1 } { 12 } & - \frac { 1 } { 5 } & \frac { 1 } { 2 } & - \frac { 1 } { 7 } \\
• 0 & - \frac { 1 } { 6 } & \frac { 1 } { 12 } & 0
• \end{array} \right]\]
• B) The inverse does not exist.
• C)
• \[\left[ \begin{array} { c c c c }
• \frac { 1 } { 6 } & - \frac { 1 } { 3 } & \frac { 1 } { 6 } & - \frac { 1 } { 4 } \\
• \frac { 1 } { 6 } & - \frac { 1 } { 2 } & - 4 & - \frac { 1 } { 3 } \\
• \frac { 1 } { 12 } & - \frac { 1 } { 5 } & \frac { 1 } { 2 } & - \frac { 1 } { 7 } \\
• 0 & - \frac { 1 } { 6 } & \frac { 1 } { 12 } & 0
• \end{array} \right]\]
• D)
• \[\left[ \begin{array} { r r r r }
• 1 & 0 & 0 & - \frac { 2 } { 3 } \\
• 0 & 1 & 0 & - \frac { 1 } { 4 } \\
• 0 & 0 & 1 & - \frac { 1 } { 8 } \\
• 0 & 0 & 0 & 0
• \end{array} \right]\]

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Definitions:

Debtor

An individual or entity that owes money to another party, often a lender or creditor.

Perfection

In the context of secured transactions, perfection is the legal process by which a secured creditor establishes its priority interest in the debtor's collateral over other claimants.

Legal Steps

Sequential actions or procedures that are taken in accordance with law to achieve a legal outcome, such as filing a lawsuit or executing a contract.

Collateral

Assets or property offered as security for the repayment of a loan, subject to seizure on default.