If the system of linear equations 2 x + 3 y - z = - 2 x + y + z = 4 x - y + λ z = 4 λ - 4 where λ ∈ ℝ , has no solution, then

Step-by-step solution

If we have three equations in three variables, a 1 x + b 1 y + c 1 z = d 1 a 2 x + b 2 y + c 2 z = d 2 a 3 x + b 3 y + c 3 z = d 3 then ∆ = a 1 b 1 c 1 a 2 b 2 c 2 a 3 b 3 c 3 , ∆ 1 = d 1 b 1 c 1 d 2 b 2 c 2 d 3 b 3 c 3 , ∆ 2 = a 1 d 1 c 1 a 2 d 2 c 2 a 3 d 3 c 3 , ∆ 3 = a 1 b 1 d 1 a 2 b 2 d 2 a 3 b 3 d 3 . If the set of equations do not have a solution then ∆ = 0 and at least one among ∆ 1 , ∆ 2 , ∆ 3 is not equal to zero. ∆ = 2 3 - 1 1 1 1 1 - 1 λ = 0 &#