The system of linear equations
x+λy−z=0λx−y−z=0x+y−λz=0
has a non-trivial solution for :
exactly one value of .
exactly two value of .
exactly three value of .
infinitely many values of .
∣∣ ∣∣1λ−1λ−1−111−λ∣∣ ∣∣=0
1(λ+1)−λ(−λ2+1)+1(−λ−1)=0λ3−λ+λ+1−λ−1=0λ3−λ=0λ(λ2−1)=0λ=0,λ=±1
Exactly three values of λ