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

LetΔ=α111α111α              C1→C1+C2+C3          =α+211α+2α1α+21α         =(α+2) 1111α111α                R1→R1−R2, R2→R2−R3        =(α+2)01-α00α-11-α11α =α+2o(αα-1-11-α)−(1−α)0−(1−α)         =(α+2)(1−α)2If α=1the system of equations has infinitely many solutions If α=−2, on adding 3 equations we obtain 0=-9∴ The system has no solution for α=−2