αx+y+z=α−1x+αy+z=α−1x+y+zα=α−1Δ=α111α111α=α(α2−1)−1(α−1)+1(1−α)=α(α−1)(α+1)−1(α−1)−1(α−1)⇒(α−1)[α2+α−1−1]=0⇒(α−1)[α2+α−2]=0[α2+2α−α−2]=0(α−1)[α(α+2)−1(α+2)]=0(α−1)=0,α+2=0⇒α=−2,1; but α=1
The system of equations αx+y+z=α−1x+αy+z=α−1x+y+αz=α−1 has no solution, if α is
Held on 30 Apr 2005 · Verified 6 Jul 2026.
−2
either −2 or 1
not -2
1
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