Question

Select the correct option from the given alternatives:

The value of a for which system of equation a³x + (a + 1)³ y + (a + 2)³z = 0 ax + (a +1)y + (a + 2)z = 0 and x + y + z = 0 has non zero Soln. is

पर्याय

• 0

• –1

• 1

• 2

Answer 1

–1

Explanation:

The given system of equations will have a non-zero solution, if

`|("a"^3, ("a" + 1)^3, ("a" + 2)^3),("a", "a" + 1, "a" + 2),(1, 1, 1)|` = 0

Applying C₂ → C₂ – C₁, C₃ → C₃  – C₂, we get

`|("a"^3, 3"a"^2 + 3"a" + 1, 3"a"^2 + 9"a" + 7),("a", 1, 1),(1, 0, 0)|` = 0

∴ a³(0 – 0) – (3a² + 3a + 1) (0 – 1) + (3a² + 9a + 7) (0 – 1) = 0

∴ –6a – 6 = 0,

∴ a = – 1