Question

If Δ = `|(0, "b" - "a", "c" - "a"),("a" - "b", 0, "c" - "b"),("a" - "c", "b" - "c", 0)|`, then show that ∆ is equal to zero.

Answer 1

Interchanging rows and columns, we get

Δ = `|(0, "a" - "b", "a" - "c"),("b" - "a", 0, "b" - "c"),("c" - "a", "c" - "b", 0)|`

Taking ‘–1’ common from R₁, R₂ and R₃, we get

Δ = `(-1)^3|(0, "b" - "a", "c" - "a"),("a" - "b", 0, "c" - "b"),("a" - "c", "b" - "c", 0)|`

= – Δ

⇒ 2Δ = 0 or Δ = 0