Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular.
-$A = \left[ \begin{array} { c c c }
- \frac { 1 } { 4 } & - \frac { 1 } { 2 } & - \frac { 1 } { 4 } \
- \frac { 3 } { 8 } & - \frac { 1 } { 4 } & \frac { 1 } { 8 } \
\frac { 17 } { 16 } & \frac { 7 } { 8 } & \frac { 5 } { 16 }
\end{array} \right]$

A) $A ^ { - 1 } = \left[ \begin{array} { l l l } 3 & - 1 & 2 \ 4 & - 3 & 2 \ 1 & - 5 & 2 \end{array} \right]$
B) $A ^ { - 1 } = \left[ \begin{array} { l l l } 3 & - 4 & 1 \ 1 & - 3 & 5 \ 2 & - 2 & 2 \end{array} \right]$
C) $A ^ { - 1 } = \left[ \begin{array} { r r r } 3 & 1 & 2 \ - 4 & - 3 & - 2 \ 1 & 5 & 2 \end{array} \right]$
D) Singular matrix

Question

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular.
-$A = \left[ \begin{array} { c c c } 
- \frac { 1 } { 4 } & - \frac { 1 } { 2 } & - \frac { 1 } { 4 } \
- \frac { 3 } { 8 } & - \frac { 1 } { 4 } & \frac { 1 } { 8 } \
\frac { 17 } { 16 } & \frac { 7 } { 8 } & \frac { 5 } { 16 }
\end{array} \right]$

A) $A ^ { - 1 } = \left[ \begin{array} { l l l } 3 & - 1 & 2 \ 4 & - 3 & 2 \ 1 & - 5 & 2 \end{array} \right]$
B) $A ^ { - 1 } = \left[ \begin{array} { l l l } 3 & - 4 & 1 \ 1 & - 3 & 5 \ 2 & - 2 & 2 \end{array} \right]$
C) $A ^ { - 1 } = \left[ \begin{array} { r r r } 3 & 1 & 2 \ - 4 & - 3 & - 2 \ 1 & 5 & 2 \end{array} \right]$
D) Singular matrix

Quizplus · Accepted Answer

To determine if a matrix is invertible, we check if its determinant is non-zero. The determinant of matrix A is non-zero, indicating it is invertible. The provided matrices as potential inverses must satisfy the equation $AA^{-1} = I$, where $I$ is the identity matrix. By performing the matrix multiplication with each option, we find that option C gives the identity matrix when multiplied by A, confirming it as the correct inverse.

Determine the Inverse of the Given Matrix, If Possible A) A−1=[3−124−321−52]A ^ { - 1 } = \left[ \begin{array} { l l l } 3 & - 1 & 2 \\ 4 & - 3 & 2 \\ 1 & - 5 & 2 \end{array} \right]A−1=​341​−1−3−5​222​​

Determine the Inverse of the Given Matrix, If Possible A) $A ^ { - 1 } = \left[ \begin{array} { l l l } 3 & - 1 & 2 \\ 4 & - 3 & 2 \\ 1 & - 5 & 2 \end{array} \right]$