If the system of equations x - k y + 3 z = 0 , 2 x + k y - 2 z = 0 and 3 x - 4 y + 2 z = 0 has non-trivial solutions, then the value of 10 y x is equal to

Step-by-step solution

For non-trivial solutions, 1 - k       3 2       k - 2 3 - 4       2 = 0 ⇒ 2 k - 8 + k 10 + 3 - 8 - 3 k = 0 ⇒ 3 k - 32 = 0 ⇒ k = 32 3 Putting z = λ , we get, 3 x - 32 y = - 9 λ 3 x - 4 y = - 2 λ y = λ 4 x = - λ 3