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Question
Write Minors and Cofactors of the elements of the following determinant:
`|(a,c),(b,d)|`
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Solution
The given determinant is `|(a,c),(b,d)|`.
Minor of element aij is Mij.
∴ M11 = Minor of element a11 = d
M12 = Minor of element a12 = b
M21 = Minor of element a21 = c
M22 = Minor of element a22 = a
Cofactor of aij is Aij = (−1)i + j Mij.
A11 = (−1)1+1 M11
= (−1)2 (d)
= d
A12 = (−1)1+2 M12
= (−1)3 (b)
= −b
A21 = (−1)2+1 M21
= (−1)3 (c)
= −c
A22 = (−1)2+2 M22
= (−1)4 (a)
= a
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