Let the system of linear equations x + 2 y + z = 2 , α x + 3 y - z = α , - α x + y + 2 z = - α be inconsistent. Then α is equal to

Step-by-step solution

Given, the system of linear equations x + 2 y + z = 2 , α x + 3 y - z = α , and - α x + y + 2 z = - α Now for system to be inconsistent, ∆ = 0   &   either of    ∆ 1 , ∆ 2   or   ∆ 3   ≠ 0 So, Δ = 1 2 1 2 3 - 1 - 2 1 2 = 6 + y - 2 2 α - α + 1 α + 3 α = 7 - 2 α + 4 α = 7 + 2 α Δ = 0 ⇒ α = - 7 2 Now calculating, Δ 1 = 2 2 1 α 3 - 1 - α 1 2 = 14 + 2 α