34 The system of linear equations x+λy z=0 λx y z=0 x+y λz=0 has a non-trivial solution for : - Maths - Straight Lines

Question

34 The system of linear equations x+λy−z=0
λx−y−z=0 x+y−λz=0 has a non-trivial
solution for :
(1) exactly one value of λ (2) exactly two values of
λ (3) exactly three values of λ (4) infinitely many
values of λ

Rahul Raj · Accepted Answer

dear student

the system will have non trivial solutions if∆=1λ-1λ-1-111-λ=0(λ+1)-λ(-λ2+1)-1(λ+1)=0λ3-λ=0λ(λ+1)(λ-1)=0λ=0,±1option C

regards

34. The system of linear equations x+λy−z=0 λx−y−z=0 x+y−λz=0 has a non-trivial solution for : (1) exactly one value of λ. (2) exactly two values of λ. (3) exactly three values of λ. (4) infinitely many values of λ.

34. The system of linear equations x+λy−z=0 λx−y−z=0 x+y−λz=0 has a non-trivial solution for :
(1) exactly one value of λ. (2) exactly two values of λ. (3) exactly three values of λ. (4) infinitely many values of λ.