Q.The co-factor of $-7$ in the determinant $\begin{vmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{vmatrix}$ is :

Delete row 3 and column 3, evaluate the remaining minor, and apply the $(-1)^{3+3}=+1$ sign to get cofactor $=18$.

The entry $-7$ is in the third row and third column, so $i=3,\ j=3$. Its cofactor is

$C_{33} = (-1)^{3+3}\, M_{33} = (+1)\begin{vmatrix} 2 & -3 \\ 6 & 0 \end{vmatrix}$

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