Question

If Δ1 = |(a2 + x2, ab - cx, ac + bx), (ab + cx, b2 + x2, bc + ax), (ac - bx, bc - ax, c2 + x2)| and Δ2 = |(x, c, -b), (-c, x, a), (b, -a, x)|, then

(A) Δ1 = Δ2

(B) Δ1 = Δ22

(C) Δ1 = 2Δ2

(D) of these

Answer 1

Answer is (B) Δ1 = Δ22

We have

Cofactors of 1st row are: x2 + a2, ab + cx, ac - bx

Cofactors of 2nd row are: ab - cx, x2 + b2, ac + bx

Cofactors of 3rd row are: ac + bx, bc - ax, x2 + c2

Therefore, determinant of cofactors of ∆2 is