Find the inverse of A if it has one, or state that the inverse does not exist.
-$$A = \left[ \begin{array} { l l l }
1 & 3 & 2 \
1 & 3 & 3 \
2 & 7 & 8
\end{array} \right]$$
A)
$$\left[ \begin{array} { l l l }
1 & \frac { 1 } { 3 } & \frac { 1 } { 2 } \
1 & \frac { 1 } { 3 } & \frac { 1 } { 3 } \
\frac { 1 } { 2 } & \frac { 1 } { 7 } & \frac { 1 } { 8 }
\end{array} \right]$$
B) Inverse does not exist
C)
$$\left[ \begin{array} { r r r }
- 3 & 10 & - 3 \
2 & - 4 & 1 \
- 1 & 1 & 0
\end{array} \right]$$
D)
$$\left[ \begin{array} { l l l }
- 1 & - 3 & - 2 \
- 1 & - 3 & - 3 \
- 2 & - 7 & - 8
\end{array} \right]$$

Question

Find the inverse of A if it has one, or state that the inverse does not exist.
-$$A = \left[ \begin{array} { l l l } 
1 & 3 & 2 \
1 & 3 & 3 \
2 & 7 & 8
\end{array} \right]$$
A)
$$\left[ \begin{array} { l l l } 
1 & \frac { 1 } { 3 } & \frac { 1 } { 2 } \
1 & \frac { 1 } { 3 } & \frac { 1 } { 3 } \
\frac { 1 } { 2 } & \frac { 1 } { 7 } & \frac { 1 } { 8 }
\end{array} \right]$$
B) Inverse does not exist
C)
$$\left[ \begin{array} { r r r } 
- 3 & 10 & - 3 \
2 & - 4 & 1 \
- 1 & 1 & 0
\end{array} \right]$$
D)
$$\left[ \begin{array} { l l l } 
- 1 & - 3 & - 2 \
- 1 & - 3 & - 3 \
- 2 & - 7 & - 8
\end{array} \right]$$

Quizplus · Accepted Answer

To determine if an inverse exists and to find it if it does, one can use the determinant of matrix A. If the determinant is non-zero, the inverse exists. The calculation of the inverse involves finding the matrix of cofactors, transposing it, and then dividing by the determinant. The correct inverse matrix is given in option C, indicating that the determinant of A is non-zero and the inverse has been correctly calculated.

Find the Inverse of a If It Has One, or State