Question

If A = [a_ij] = `[(2,-1,5),(1,3,2),(5,0,4)]` and c_ij is the cofactor of element a_ij, then the value of a₂₁ × c₁₁ + a₂₂ × c₁₂ + a₂₃ × c₁₃ is ______.

विकल्प

• −57

• 0

• 9

• 57

Answer 1

If A = [a_ij] = `[(2,-1,5),(1,3,2),(5,0,4)]` and c_ij is the cofactor of element a_ij, then the value of a₂₁ × c₁₁ + a₂₂ × c₁₂ + a₂₃ × c₁₃ is 0.

Explanation:

Given, `A = [a_(ij)] = [(2,-1,5),(1,3,2),(5,0,4)]`

a₂₁ = 1, a₂₂ = 3, a₂₃ = 2

`c_11 = (-1)^(1+1)|(3,2),(0,4)|`

= (1) (12 − 0)

= 12

`c_12 = (-1)^(1+2)|(1,2),(5,4)|`

= (−1) (4 − 10)

= (−1) (−6)

= 6

`c_13 = (-1)^(1+3)|(1,3),(5,0)|`

= (1) (0 − 15)

= −15

Now, a₂₁c₁₁ + a₂₂c₁₂ + a₂₃c₁₃ = (1)(12) + (3)(6) + (2)(-15)

= 12 + 18 − 30

= 30 − 30

= 0