If |{-a^2 ab ac} {ab -b^2 bc} {ac bc -c^2}| = k a^2 b^2 c^2, then k is equal to

Question

If \(\begin{vmatrix}-a^2 &ab& ac\\ab& -b^2 & bc\\ac& bc& -c^2 \end{vmatrix}\) = k a² b² c², then k is equal to

(a) –4

(b) 2

(c) 4

(d) 8

Answer 1

Correct option is (c) 4

(Taking out a, b, c common from R₁, R₂, R₃ respectively)

(Taking out a, b, c common from C₁, C₂, C₃ respectively)

= 4a² b² c² (Expanding along C₁)

∴ k = 4