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Question
Write the adjoint of the matrix \[A = \begin{bmatrix}- 3 & 4 \\ 7 & - 2\end{bmatrix} .\]
Solution
\[\text{ Let }C_{ij} \text{ be a cofactor of }a_{ij}\text{ in A .} \]
Now,
\[ C_{11} = - 2\]
\[ C_{12} = - 7\]
\[ C_{21} = - 4\]
\[ C_{22} = - 3\]
\[ \therefore adj A = \begin{bmatrix}- 2 & - 7 \\ - 4 & - 3\end{bmatrix}^T = \begin{bmatrix}- 2 & - 4 \\ - 7 & - 3\end{bmatrix}\]
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