Question

Find the minors and cofactors of all the elements of the following determinant.

`|(1,-3,2),(4,-1,2),(3,5,2)|`

Answer 1

Minor of 1 is M₁₁ = `|(-1,2),(5,2)|` = -2 – 10 = -12

Minor of -3 is M₁₂ = `|(4,2),(3,2)|` = 8 - 6 = 2

Minor of 2 is M₁₃ = `|(4,-1),(3,5)|` = 20 + 3 = 23

Minor of 4 is M₂₁ = `|(-3,2),(5,2)|` = - 6 - 10 = - 16

Minor of -1 is M₂₂ = `|(1,2),(3,2)|` = 2 - 6 = - 4

Minor of 2 is M₂₃ = `|(1,-3),(3,5)|` = 5 + 9 = 14

Minor of 3 is M₃₁ = `|(-3,2),(-1,2)|` = - 6 + 2 = - 4

Minor of 5 is M₃₂ = `|(1,2),(4,2)|` = 2 - 8 = - 6

Minor of 2 is M₃₃ = `|(1,-3),(4,-1)|`= - 1 + 12 = 11

Cofactor of 1 is A₁₁ = (-1)¹⁺¹ M₁₁ = -12
Cofactor of -3 is A₁₂ = (-1)¹⁺² M₁₂ = -2
Cofactor of 2 is A₁₃ = (-1)¹⁺³ M₁₃ = 23
Cofactor of 4 is A₂₁ = (-1)²⁺¹ M₂₁ = -1 × -16 = 16
Cofactor of -1 is A₂₂ = (-1)²⁺² M₂₂ = -4
Cofactor of 2 is A₂₃ = (-1)²⁺³ M₂₃ = -14
Cofactor of 3 is A₃₁ = (-1)³⁺¹ M₃₁ = -4
Cofactor of 5 is A₃₂ = (-1)³⁺² M₃₂ = -1 × -6 = 6
Cofactor of 2 is A₃₃ = (-1)³⁺³ M₃₃ = 11