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Question

The system of equations. ar+y+z=a1, x+ay+z=a1 and x+y+az=a1 doesn't have unique solution if a=

A
1 or 2
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B
3
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C
2
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D
1
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Solution

The correct option is A 1 or 2
The condition for system of equations, to not have unique solution, is

Δ=0

Given,

a111a111a

deta111a111a

=adet(a11a)1det(111a)+1det(1a11)

=a(a21)1(a1)+1(1a)

=a33a+2

a33a+2=0

(a1)2(a+2)=0

a=1,a=2

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