Write Minors and Cofactors of the elements of following determinants:
(i) $\left|\begin{array}{rr}2 & -4 \\ 0 & 3\end{array}\right|$
(ii) $\left|\begin{array}{ll}a & c \\ b & d\end{array}\right|$
(i) The given determinant is $\left|\begin{array}{rr}2 & -4 \\ 0 & 3\end{array}\right|$.
Minor of element $a_{i j}$ is $M_{i j}$.
$\therefore \mathrm{M}_{11}=$ minor of element $a_{11}=3$
$M_{12}=$ minor of element $a_{12}=0$
$M_{21}=$ minor of element $a_{21}=-4$
$M_{22}=$ minor of element $a_{22}=2$
Cofactor of $a_{i j}$ is $A_{i j}=(-1)^{\gamma+j} M_{i j}$.
$\therefore A_{11}=(-1)^{1+1} M_{11}=(-1)^{2}(3)=3$
$A_{12}=(-1)^{1+2} M_{12}=(-1)^{3}(0)=0$
$A_{21}=(-1)^{2+1} M_{21}=(-1)^{3}(-4)=4$
$A_{22}=(-1)^{2+2} M_{22}=(-1)^{4}(2)=2$
(ii) The given determinant is $\left|\begin{array}{ll}a & c \\ b & d\end{array}\right|$.
Minor of element $a_{i j}$ is $M_{i j}$.
$\therefore \mathrm{M}_{11}=$ minor of element $a_{11}=d$
$M_{12}=$ minor of element $a_{12}=b$
$M_{21}=$ minor of element $a_{21}=c$
$\mathrm{M}_{22}=$ minor of element $\mathrm{a}_{22}=\mathrm{a}$
Cofactor of $a_{i j}$ is $A_{i j}=(-1)^{j+j} M_{i j}$.
$\therefore \mathrm{A}_{11}=(-1)^{1+1} \mathrm{M}_{11}=(-1)^{2}(d)=d$
$\mathrm{~A}_{12}=(-1)^{1+2} \mathrm{M}_{12}=(-1)^{3}(b)=-b$
$\mathrm{~A}_{21}=(-1)^{2+1} \mathrm{M}_{21}=(-1)^{3}(c)=-c$
$\mathrm{~A}_{22}=(-1)^{2+2} \mathrm{M}_{22}=(-1)^{4}(a)=a$
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