Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { l l l }
1 & 1 & 1 \
2 & 1 & 1 \
2 & 2 & 3
\end{array} \right]$$
A)
$$\left[ \begin{array} { l l l }
- 1 & - 1 & - 1 \
- 2 & - 1 & - 1 \
- 2 & - 2 & - 3
\end{array} \right]$$
B)
$$\left[ \begin{array} { r r r }
- 1 & 1 & 0 \
4 & - 1 & - 1 \
- 2 & 0 & 1
\end{array} \right]$$
C)
$$\left[ \begin{array} { c c c }
1 & 1 & 1 \
\frac { 1 } { 2 } & 1 & 1 \
\frac { 1 } { 2 } & \frac { 1 } { 2 } & \frac { 1 } { 3 }
\end{array} \right]$$

D) The inverse does not exist.

Question

Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { l l l } 
1 & 1 & 1 \
2 & 1 & 1 \
2 & 2 & 3
\end{array} \right]$$
A)
$$\left[ \begin{array} { l l l } 
- 1 & - 1 & - 1 \
- 2 & - 1 & - 1 \
- 2 & - 2 & - 3
\end{array} \right]$$
B)
$$\left[ \begin{array} { r r r } 
- 1 & 1 & 0 \
4 & - 1 & - 1 \
- 2 & 0 & 1
\end{array} \right]$$
C)
$$\left[ \begin{array} { c c c } 
1 & 1 & 1 \
\frac { 1 } { 2 } & 1 & 1 \
\frac { 1 } { 2 } & \frac { 1 } { 2 } & \frac { 1 } { 3 }
\end{array} \right]$$

D) The inverse does not exist.

Quizplus · Accepted Answer

To find the inverse of a matrix, one can use the method of augmenting the given matrix with the identity matrix and then applying row operations to reduce the given matrix to the identity matrix. The operations performed on the given matrix will transform the identity matrix into the inverse of the given matrix. The correct inverse matrix is option B, as it is the result of performing such operations on the given matrix.

Find the Inverse, If It Exists, for the Matrix [111211223]\left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]​122​112​113​​

Find the Inverse, If It Exists, for the Matrix $\left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]$