The system of linear equations x + λ y - z = 0 λ x - y - z = 0 x + y - λ z = 0 has a non…

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 two values of λ
  2. Exactly three values of λ
  3. Infinitely many values of λ
  4. Exactly one value of λ

Solution

For non - trivial solution.

Δ=1λ-1λ-1-111-λ=0

1λ+1-λ-λ2+1-1λ+1=0

λ+1-λ1-λ 1+λ-λ+1=0

λ1-λ 1+λ=0 

λ=0, λ=1, λ= -1

Exactly there value of λ.

Asked in: JEE Main 2016 (03 Apr)

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