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Q.
If $\Delta=\begin{vmatrix}a & h & g \\ h & b & f \\ g & f & c\end{vmatrix}$, then the cofactor $A_{21}$ is
Determinants
Solution:
We have, $\Delta=\begin{vmatrix}a & h & g \\ h & b & f \\ g & f & c\end{vmatrix}$
Now, minor of $a_{21}$ is
$M_{21}=\begin{vmatrix}h & g \\ f & c\end{vmatrix}=h c-f g$
$\therefore A_{21}=(-1)^{2+1} M_{21}=-(h c-f g)=f g-h c$