The system of equationsαx+y+z= α−1,   x+αy+z=α−1x+y+αz=α−1 has no solution if  α is

The condition for non-existance of solution is Δ=0 ⇒α111α111α=0⇒ α(α2−1)−1(α−1)+1(1−α)=0⇒ α3−3α +2=0  ⇒α=−2,  1  If α=1, all are coincident It has infinitely many solutions  ∴α=−2