Write Minors and Cofactors of elements of following determinants : left|begin{array}{rr}2 & -4 0

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3 and 4 .Determinants and Matrices

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Write Minors and Cofactors of the elements of following determinants : $\left|\begin{array}{rr}2 & -4 \\ 0 & 3\end{array}\right|$

Option A

Option B

Option C

Option D

Solution

The given determinant is $\left|\begin{array}{cc}2 & -4 \\ 0 & 3\end{array}\right|$

Minor of element $a_{ij}$ is $M_{ij}$

$\therefore \mathrm{M}_{11}=$ minor of element $a_{11}=3$

$\mathrm{M}_{12}=$ minor of element $a_{12}=0$

$\mathrm{M}_{21}=$ minor of element $a_{21}=-4$

$\mathrm{M}_{22}=$ minor of element $a_{22}=2$

Cofactor of $a_{ij}$ is $A_{ij}=(-1)^{i+j} M_{i j}$

$\therefore A_{11}=(-1)^{1+1} M_{11}=(-1)^{2}(3)=3$

$A_{12}=(-1)^{1+2} M_{12}=(-1)^{3}(0)=0$

$A_{21}=(-1)^{2+1} M_{21}=(-1)^{3}(-4)=4$

$A_{22}=(-1)^{2+2} M_{22}=(-1)^{4}(2)=2$

Standard 12

Mathematics

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