Question

If A_ij denotes the cofactor of the element a_ij of the determinant `|(2, -3, 5),(6, 0, 4),(1, 5, -7)|`, then value of a₁₁A₃₁ + a₁₂A₃₂ + a₁₃A₃₃ is ______.

Options

• 0

• 5

• 10

• – 5

Answer 1

If A_ij denotes the cofactor of the element a_ij of the determinant `|(2, -3, 5),(6, 0, 4),(1, 5, -7)|`, then value of a₁₁A₃₁ + a₁₂A₃₂ + a₁₃A₃₃ is 0.

Explanation:

Given determinant is `|(2, -3, 5),(6, 0, 4),(1, 5, -7)|`

We have M₃₁ = `|(-3, 5),(0, 4)|`

= – 12 – 0

= – 12

`\implies` A₃₁ = M₃₁ = – 12

M₃₂ = `|(2, 5),(6, 4)|`

= 8 – 30

= – 22

`\implies` A₃₂ = – M₃₂ = 22

M₃₃ = `|(2, -3),(6, 0)|`

= 0 + 18

= 18

`\implies` A₃₃ = M₃₃ = 18

∴ a₁₁A₃₁ + a₁₂A₃₂ + a₁₃A₃₃ 

= (2)(– 12) + (– 3)(22) + (5)(18)

= – 24 – 66 + 90

= – 90 + 90

= 0