    Question

# The system of linear equations x+λy−z=0; λx−y−z=1; x+y−λz=0 has a non - trivial solution for

A
infinitely many values of λ
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B
exactly one value of λ
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C
exactly two values of λ
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D
exactly three values of λ
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Solution

## The correct option is D exactly three values of λGiven, system of linear equation is x+λy−z=0; λx−y−z=0; x+y−λz=0 Note that, given system will have a non - trivial solution only if determinant of coefficient matrix is zero, i.e. ∣∣ ∣∣1λ−1λ−1−111−λ∣∣ ∣∣=0 ⇒ 1(λ+1)−λ(−λ2+1)−1(λ+1)=0⇒ λ+1+λ3−λ−λ−1=0⇒ λ3−λ=0⇒(λ2−1)=0⇒ λ=0 or λ=±1 Hence, given system of linear equation has a non - trivial solution for exactly three values of λ  Suggest Corrections  0      Similar questions  Related Videos   Applications
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