Determine the Inverse of the Given Matrix, If Possible $$A = \left[ \begin{array} { r r r } 4 & - 1 & 5 \\1 & 1 & - 2 \\- 1 & 1 & 0\end{array} \right]$$

question 20

Multiple Choice

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular.
- $$A = \left[ \begin{array} { r r r } 4 & - 1 & 5 \\1 & 1 & - 2 \\- 1 & 1 & 0\end{array} \right]$$

• A) \(A ^ { - 1 } = \left[ \begin{array} { c c c } \frac { 1 } { 8 } & \frac { 5 } { 16 } & - \frac { 3 } { 16 } \\ \frac { 1 } { 8 } & \frac { 5 } { 16 } & \frac { 13 } { 16 } \\ \frac { 1 } { 8 } & - \frac { 3 } { 16 } & - \frac { 5 } { 16 } \end{array} \right]\)
• B) Singular matrix
• C) \(A ^ { - 1 } = \left[ \begin{array} { c c c } - \frac { 1 } { 8 } & \frac { 5 } { 16 } & - \frac { 3 } { 16 } \\ - \frac { 1 } { 8 } & \frac { 5 } { 16 } & \frac { 13 } { 16 } \\ - \frac { 1 } { 8 } & - \frac { 3 } { 16 } & \frac { 5 } { 16 } \end{array} \right]\)
• D) \(A ^ { - 1 } = \left[ \begin{array} { c c c } \frac { 1 } { 8 } & \frac { 5 } { 16 } & - \frac { 3 } { 16 } \\ \frac { 1 } { 8 } & \frac { 5 } { 16 } & \frac { 13 } { 16 } \\ \frac { 1 } { 8 } & - \frac { 3 } { 16 } & \frac { 5 } { 16 } \end{array} \right]\)

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Definitions:

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