Question

Choose the correct option:

If a, b, c are in A.P. then the determinant `[(x + 2, x + 3, x + 2a),(x + 3, x + 4, x + 2b),(x + 4, x + 5, x + 2c)]` is

विकल्प

• 0

• 1

• x

• 2x

Answer 1

0

Explanation:

Given Δ = `[(x + 2, x + 3, x + 2a),(x + 3, x + 4, x + 2b),(x + 4, x + 5, x + 2c)]`

= `[(x + 2, x + 3, x + 2a),(x + 3, x + 4, x + (a + c)),(x + 4, x + 5, x + 2c)]`  ......(Since a, b and c are in A.P., 2b = a + c)

Applying R₁ `→` R₁ – R₂ and R₃ `→` R₁  - R₂ 

Δ = `[(-1, -1, a - c),(x + 3, x + 4, x + (a + c)),(1, 1, c - a)]`

Applying R₁ `→` R₁ + R₃ 

Δ = `|(0, 0, 0),(x + 3, x + 4, x + (a + c)),(1, 1, c - a)|` = 0