Find the inverse of 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) No inverse

Question

Find the inverse of 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) No inverse

Quizplus · Accepted Answer

To find the inverse of a matrix, one typically applies the formula involving the adjugate matrix and the determinant of the original matrix. The determinant of the given matrix is non-zero, indicating that an inverse exists. By calculating the inverse through standard methods (e.g., using the adjugate matrix and dividing by the determinant), option B is found to be the correct inverse of the given matrix.

Find the Inverse of 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 of the Matrix $\left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]$