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Question

# Number of values of ′λ′ for which the system of linear equations λx+y+z=1, x+λy+z=0, x+y+λz=0 has infinitely many solutions are

A
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B
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C
2
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D
3
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Solution

## The correct option is C 3Givenequationarex+λy−z=0λx−y−z=0x+y−λz=0Thegivensystemwillhaveanon−trivialsolutiononlyiftheerminatsofthecoefficientmatrixiszero∣∣ ∣∣1λ−1λ−1−111−λ∣∣ ∣∣=0⇒1(λ+1)+λ(−λ2+1)−1(λ+1)=0⇒λ3−λ=0⇒λ(λ2+1)=0∴λ=0andλ=±iSo,givensystemoflinearequationhasanon−trivialsolutionforexcatlythreesolutionofλ.Hence, this is the answer.

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