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Question
If \[A = \begin{bmatrix}5 & 6 & - 3 \\ - 4 & 3 & 2 \\ - 4 & - 7 & 3\end{bmatrix}\] , then write the cofactor of the element a21 of its 2nd row.
Solution
We have
\[A = \begin{bmatrix}5 & 6 & - 3 \\ - 4 & 3 & 2 \\ - 4 & - 7 & 3\end{bmatrix}\]
Here, a21 = −4
The cofactor of the element a21 = −4 is given by
\[C_{21} = \left( - 1 \right)^\left( 2 + 1 \right) \begin{vmatrix}6 & - 3 \\ - 7 & 3\end{vmatrix} = - 1\left( 18 - 21 \right) = 3\]
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