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)
$$\left[ \begin{array} { c c c }
1 & 1 & 1 \
\frac { 1 } { 2 } & 1 & 1 \
\frac { 1 } { 2 } & \frac { 1 } { 2 } & \frac { 1 } { 3 }
\end{array} \right]$$

B) The inverse does not exist.

C)
$$\left[ \begin{array} { l l l }
- 1 & - 1 & - 1 \
- 2 & - 1 & - 1 \
- 2 & - 2 & - 3
\end{array} \right]$$

D)

$$\left[ \begin{array} { r r r }
- 1 & 1 & 0 \
4 & - 1 & - 1 \
- 2 & 0 & 1
\end{array} \right]$$

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)
$$\left[ \begin{array} { c c c } 
1 & 1 & 1 \
\frac { 1 } { 2 } & 1 & 1 \
\frac { 1 } { 2 } & \frac { 1 } { 2 } & \frac { 1 } { 3 }
\end{array} \right]$$

B) The inverse does not exist.

C)
$$\left[ \begin{array} { l l l } 
- 1 & - 1 & - 1 \
- 2 & - 1 & - 1 \
- 2 & - 2 & - 3
\end{array} \right]$$

D)

$$\left[ \begin{array} { r r r } 
- 1 & 1 & 0 \
4 & - 1 & - 1 \
- 2 & 0 & 1
\end{array} \right]$$

Quizplus · Accepted Answer

To find the inverse of a matrix, one common method is to apply the Gauss-Jordan elimination on the augmented matrix [A|I], where A is the given matrix and I is the identity matrix of the same size. The inverse exists if and only if the determinant of the matrix is non-zero. In this case, the determinant of the given matrix is non-zero, indicating that an inverse exists. The correct inverse is calculated through this process or by using the formula for the inverse of a 3x3 matrix, which involves the matrix of cofactors, transposing that matrix, and then dividing by the determinant of the original matrix. The correct answer is option D, as it is the result of such a calculation.

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 $\left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]$