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

question 29

Multiple Choice

Find the inverse of the matrix A, if it exists.
- $$A = \left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]$$

• A) \(A ^ { - 1 }\) does not exist.
• B) \(A ^ { - 1 } = \left[ \begin{array} { r r r } - 1 & 1 & 0 \\ 4 & - 1 & - 1 \\ - 2 & 0 & 1 \end{array} \right]\)
• C) \(\mathrm { A } ^ { - 1 } = \left[ \begin{array} { c c c } 1 & 1 & 1 \\ \frac { 1 } { 2 } & 1 & 1 \\ \frac { 1 } { 2 } & \frac { 1 } { 2 } & \frac { 1 } { 3 } \end{array} \right]\)
• D) \(A ^ { - 1 } = \left[ \begin{array} { l l l } - 1 & - 1 & - 1 \\ - 2 & - 1 & - 1 \\ - 2 & - 2 & - 3 \end{array} \right]\)

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