The number of values of α for which the system of equations x + y + z = α α x + 2 α y + 3 z = - 1 x + 3 α y + 5 z = 4 is inconsistent, is

Step-by-step solution

Given linear equations are x + y + z = α α x + 2 α y + 3 z = - 1 x + 3 α y + 5 z = 4 For this system of linear equations to have inconsistent solution D = 1 1 1 α 2 α 3 1 3 α 5 = 0 ⇒ α - 1 2 = 0 ⇒ α = 1 Now for α = 1 D 1 = 1 1 1 - 1 2 3 4 3 5 = 10 - 9 - - 5 - 12 + - 3 - 8 = 1 + 17 - 11 ≠ 0 Hence, for α = 1 the system of equation has inconsistent solution.