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Write Minors and Cofactors of the elements of following determinants: (i) determinant 2 -4 0 3

Q : 1     Write Minors and Cofactors of the elements of following determinants:

          \small (i) \begin{vmatrix}2 &-4 \\0 &3 \end{vmatrix}

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GIven determinant: \begin{vmatrix}2 &-4 \\0 &3 \end{vmatrix}

Minor of element a_{ij} is M_{ij}.

Therefore we have 

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

and finding cofactors of a_{ij} is  A_{ij} = (-1)^{i+j}M_{ij}.

Therefore we have:

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

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