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Question
Write the cofactor of a12 in the following matrix \[\begin{bmatrix}2 & - 3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & - 7\end{bmatrix} .\]
Solution
\[\text{ Given: }\begin{bmatrix}2 & - 3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & - 7\end{bmatrix}\]
Here,
\[ a_{12} = - 3\]
\[\text{ Cofactor of }a_{12} = \left( - 1 \right)^{1 + 2} \begin{vmatrix}6 & 4 \\ 1 & - 7\end{vmatrix} = - ( - 42 - 4) = 46\]
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