For the system of equations x + y + z = 6 x + 2 y + α z = 10 x + 3 y + 5 z = β , which one of the following is NOT true?

Step-by-step solution

Given, the system of equations x + y + z = 6 x + 2 y + α z = 10 x + 3 y + 5 z = β Now finding, △ = 1 1 1 1 2 α 1 3 5 ⇒ △ = 1 10 - 3 α - 5 - α + 3 - 2 ⇒ △ = 6 - 2 α Now for unique solution, △ ≠ 0 ⇒ α ≠ 3 So, for unique solution ⇒ α ≠ 3 But in option D , system has unique solution for α = 3 which is completely wrong.