The number of integral value(s) of k such that the system of equations k x - 2 y - z = x , k y - z = z + 3 x and 2 x + k z = 2 y - z has non-trivial solution, is/are

Step-by-step solution

Rearranging all the equations, we get, k - 1 x - 2 y - z = 0 3 x - k y + 2 z = 0 2 x - 2 y + k + 1 z = 0 For a non-trivial solution, k - 1 - 2 - 1 3 - k 2 2 - 2 k + 1 = 0 ⇒ k - 1 - k 2 - k + 4 + 2 3 k - 1 - 1 - 6 + 2 k = 0 ⇒ - k 3 - k 2 + 4 k + k 2 + k - 4 + 6 k - 2 + 6 - 2 k = 0 ⇒ - k 3 + 9 k = 0 ⇒ k = 0 , - 3 , 3