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

question 183

Multiple Choice

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

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Definitions:

Carbocation Rearrangement

A process in which a carbocation intermediate undergoes structural reorganization to form a more stable ion during a chemical reaction.

Hg(OAc)2

Mercury(II) acetate, a compound used as a reagent in organic synthesis, particularly in oxymercuration-demercuration reactions.

Sodium Borohydride

A chemical reagent and reducing agent that is widely used in the reduction of aldehydes, ketones, and acyl chlorides to alcohols.

Transformation

A process by which one chemical compound is changed into another by a chemical reaction or a physical process.