Find minors and cofactors of all elements of determinant left|begin{array}{rr}1 & -2 4 & 3en

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3 and 4 .Determinants and Matrices

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Find minors and cofactors of all the elements of the determinant $\left|\begin{array}{rr}1 & -2 \\ 4 & 3\end{array}\right|$

Option A

Option B

Option C

Option D

Solution

Solution Minor of the element $a_{i j}$ is $\mathrm{M}_{i j}$

Here $a_{11}=1 .$ So $\mathrm{M}_{11}=$ Minor of $a_{11}=3$

$\mathrm{M}_{12}=$ Minor of the element $a_{12}=4$

$\mathrm{M}_{2 \mathrm{1}}=$ Minor of the element $a_{21}=-2$

$\mathrm{M}_{22}=$ Minor of the element $a_{22}=1$

Now, cofactor of $a_{i j}$ is $\mathrm{A}_{ij}$ So

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

$A_{12}=(-1)^{1+2} M_{12}=(-1)^{3}(4)=-4$

$\mathrm{A}_{21}=(-1)^{2+1} \mathrm{M}_{21}=(-1)^{3}(-2)=2$

$\mathrm{A}_{22}=(-1)^{2+2} \mathrm{M}_{22}=(-1)^{4}(1)=1$

Standard 12

Mathematics

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