If the system of linear equations x + y + 3 z = 0 x + 3 y + k 2 z = 0 3 x + y + 3 z = 0 has a non-zero solution ( x , y , z ) for some k ∈ R , then x + y z is equal to :

Step-by-step solution

So D = 0 → 1 1 3 1 3 k 2 3 1 3 = 0    ⇒    k 2 = 9 x + y + 3   z = 0 x + 3   y + 9   z = 0 3   x + y + 3   z = 0 ( 1 ) - ( 3 ) x = 0 ⇒    y + 3 z = 0 ⇒ y z = - 3 so ,   x + y z = - 3