The value of u for which the system of equation αx+y+z=α−1x+αy+z=α−1x+y+αz=α−1 has no solution, is -----------

System of equationsαx+y+z=α−1---1x+αy+z=α−1----2x+y+αz=α−1----3Since system has no solution. Therefore, (1) Δ=0 and (2)α−1≠0α111α111α=0,α≠1R1→R1−R3,R2→R2→R3α−101−α0α−11−α11α=0 or (α−1)[α(α−1)−(1−α)]+(1−α)[−(α−1)]=0or  (α−1)[α(α−1)+(α−1)]+(α−1)2=0or  (α−1)2[(α+1)+1]=0or  α=1,1,−2 or α=1,−2Since system has no solution , α≠1∴α=-2