The system of equations k x + k + 2 y + k - 2 z = 0 , k + 2 x + k y + k + 4 z = 0 and k - 2 x + k + 4 y + k z = 0 has a non-trivial solution for

Step-by-step solution

For a non-trivial solution, ∆ = 0 k k + 2 k - 2 k + 2 k k + 4 k - 2 k + 4 k = 0 ⇒ k k 2 - k + 4 2 - k + 2 k 2 + 2 k - k 2 + 2 k - 8 + k - 2 k 2 + 6 k + 8 - k 2 + 2 k = 0 ⇒ - 8 k 2 - 16 k - 8 k - 16 + 8 k 2 - 8 k - 16 = 0 ⇒ - 32 k - 32 = 0 ⇒ k = - 1