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) $A ^ { - 1 } = \left[ \begin{array} { c c c } \frac { 1 } { 8 } & \frac { 5 } { 16 } & - \frac { 3 } { 16 } \ \frac { 1 } { 8 } & \frac { 5 } { 16 } & \frac { 13 } { 16 } \ \frac { 1 } { 8 } & - \frac { 3 } { 16 } & \frac { 5 } { 16 } \end{array} \right]$

Question

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) $A ^ { - 1 } = \left[ \begin{array} { c c c } \frac { 1 } { 8 } & \frac { 5 } { 16 } & - \frac { 3 } { 16 } \ \frac { 1 } { 8 } & \frac { 5 } { 16 } & \frac { 13 } { 16 } \ \frac { 1 } { 8 } & - \frac { 3 } { 16 } & \frac { 5 } { 16 } \end{array} \right]$

Quizplus · Accepted Answer

The determinant of matrix A is non-zero, indicating it is not singular, and the inverse can be calculated. The correct inverse is given in option D, as determined by applying the formula for finding the inverse of a 3x3 matrix, which involves finding the matrix of cofactors, transposing it, and then dividing by the determinant of the original matrix.

Determine the Inverse of the Given Matrix, If Possible A=[4−1511−2−110]A = \left[ \begin{array} { r r r } 4 & - 1 & 5 \\1 & 1 & - 2 \\- 1 & 1 & 0\end{array} \right]A=​41−1​−111​5−20​​

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