If x 0 , y 0 , z 0 is any solution of the system of equations 2 x - y - z = 1 , - x - y + 2 z = 1 and x - 2 y + z = 2 , then the value of x 0 2 - y 0 2 + 1 z 0   where ,   z 0 ≠ 0 is

Step-by-step solution

Using Cramer’s rule, we get, Δ = 2 - 1 - 1 - 1 - 1 2 1 - 2 1 Using C 1 = C 1 + C 2 + C 3 Δ = 0 - 1 - 1 0 - 1 2 0 - 2 1 = 0 Δ 1 = 1 - 1 - 1 1 - 1 2 2 - 2 1 = 0 (as C 1 and C 2 are identical) Δ 2 = 2 1 - 1 - 1 1 2 1 2 1 Using C 1 = C 1 - C 2 + C 3 = 0 1 - 1 0 1 2 0 2 1 = 0 Δ 3 = 2 - 1 1 - 1 - 1 1 1 - 2 2 = 0 (as C 2 and C 3 are identical) Therefore, infinite solutions Now, put z = λ , we get, 2 x - y = 1 + λ and - x - y = 1 - 2 λ Solving these 2 equations, we get, x = &#9