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Question

Find the value of λ for which the system of equations
(1+λ)x1+x2+x3=1
x1+(1+λ)x2+x3=1
x1+x2+(1+λ)x3=1 has infinitely many solutions.

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Solution

1+λ1111+λ1111+λ
Infinite solution
=0
R1R1R3
λ1111+λ1111+λ
λ10111+λ1111+λ
λ[λ2+2λ1(11λ)]
=λ[λ2+2λ+λ]
λ2(λ+3)
λ=0 and 3

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