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Question

The system of equations
αx+y+z=α1
x+αy+z=α1
x+y+αz=α1
has no solution if α=

A
-2
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B
either -2 or 1
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C
not -2
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D
1
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Solution

The correct option is A -2
αx+y+z=α1
x+αy+z=α1
x+y+αz=α1
Δ=∣ ∣α111α111α∣ ∣
=α(α21)1(α1)+1(1α)
=α(α1)(α+1)1(α1)1(α1)
System of equations has no solutions
(α1)(α2+α11)=0
(α1)(α2+α2)=0
(α1)(α2+2αα2)=0
(α1)2(α+2)=0
α=2,1
But α1, as otherwise system is homogeneous and has infinite solutions, so α=2.

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