Let the system of linear equations x + y + a z = 2 3 x + y + z = 4 x + 2 z = 1 have a unique solution x , y , z . If α , x , y , α and x , - y are collinear points, then the sum of absolute values of all possible values of α is

Step-by-step solution

Given, x + y + a z = 2 3 x + y + z = 4 x + 2 z = 1 Now finding, Δ = 1 1 α 3 1 1 1 0 2 = - α + 3 Δ 1 = 2 1 α 4 1 1 1 0 2 = - 3 + α Δ 2 = 1 2 α 3 4 1 1 1 2 = - α + 3 Δ 3 = 1 1 2 3 1 4 1 0 1 = 0 α ≠ - 3 , x = △ 1 △ = 1 , y = △ 2 △ = 1 , z = △ 3 △ = 0 , Now points α , 1 , 1 , α   &   1 , - 1 are collinear α 1 1 1 α 1 1 - 1 1 = 0 ⇒ α α + 1 - 1 1 - 1 + 1 - 1 - α = 0 &#945