The set of all values of λ for which the system of linear equations x - 2 y - 2 z = λ x x + 2 y +…

The set of all values of λ for which the system of linear equations
x-2y-2z=λx
x+2y+z=λy
-x-y=λz
has a non-trivial solution :
  1. is an empty set
  2. contains more than two elements
  3. is a singleton
  4. contains exactly two elements

Solution

For non-trivial solution, ∆=0.

⇒1-λ-2-212-λ1-1-1-λ=0

⇒1-λ-2λ+λ2+1+1-λ+1-1 -1+2-λ=0

⇒λ2-3λ2+3λ-1=0

⇒λ-13=0

⇒λ=1

Singleton set

Asked in: JEE Main 2019 (12 Jan Shift 2)

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