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Question
Write Minors and Cofactors of the elements of the following determinant:
`|(1,0,0),(0,1,0),(0,0,1)|`
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Solution
`|(1,0,0),(0,1,0),(0,0,1)|`
Minors:
M11 = `|(1,0),(0,1)|`
= 1 − 0
= 1
M12 = `|(0,0),(0,1)|`
= 0 − 0
= 0
M13 = `|(0,1),(0,0)|`
= 0 − 0
= 0
M21 = `|(0,0),(0,1)|`
= 0 − 0
= 0
M22 = `|(1,0),(0,1)|`
= 1 − 0
= 1
M23 = `|(1,0),(0,0)|`
= 0 − 0
= 0
M31 = `|(0,0),(1,0)|`
= 0 − 0
= 0
M32 = `|(1,0),(0,0)|`
= 0 − 0
= 0
M33 = `|(1,0),(0,1)|`
= 1 − 0
= 1
Cofactors:
A11 = (−1)1+1 M11
= 1 × 1
= 1
A12 = (−1)1+2 M12
= (−1) × 0
= 0
A13 = (−1)1+3 M13
= 1 × 0
= 0
A21 = (−1)2+1 M21
= (−1) × 0
= 0
A22 = (−1)2+2 M22
= 1 × 1
= 1
A23 = (−1)2+3 M23
= (−1) × 0
= 0
A31 = (−1)3+1 M31
= 1 × 0
= 0
A32 = (−1)3+2 M32
= (−1) × 0
= 0
A33 = (−1)3+3 M33
= 1 × 1
= 1
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