Determine the Inverse of the Given Matrix, If Possible $$A = \left[ \begin{array} { l l } - 3 & 4 \\- 5 & 3\end{array} \right]$$

question 10

Multiple Choice

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular.
- $$A = \left[ \begin{array} { l l } - 3 & 4 \\- 5 & 3\end{array} \right]$$

• A) \(A ^ { - 1 } = \left[ \begin{array} { c c } \frac { 3 } { 11 } & \frac { 4 } { 11 } \\ - \frac { 5 } { 11 } & - \frac { 3 } { 11 } \end{array} \right]\)
• B) \(A ^ { - 1 } = \left[ \begin{array} { c c } \frac { 3 } { 11 } & - \frac { 4 } { 11 } \\ \frac { 5 } { 11 } & - \frac { 3 } { 11 } \end{array} \right]\)
• C) Singular matrix
• D) \(A ^ { - 1 } = \left[ \begin{array} { c c } - \frac { 3 } { 11 } & \frac { 4 } { 11 } \\ - \frac { 5 } { 11 } & \frac { 3 } { 11 } \end{array} \right]\)

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Definitions:

Fixed Overhead

Regular, unchanging costs that a business incurs, regardless of the level of production or sales activity, such as rent and salaries.

Direct Labor

The work of employees that can be directly attributed to the production of goods or services.

Fixed Overhead

Regular, fixed expenses associated with the operations of a business that do not vary with production volume.

Raw Material

Basic materials used in the production process of goods, often processed in intermediate steps before fabrication of the final product.