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The system of equationsαx+y+z=α1,   x+αy+z=α1x+y+αz=α1 has no solution if  α is  

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a
-2
b
either -2 or 1
c
not -2
d
1

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detailed solution

Correct option is A

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


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