Let S be the set of all λ ∈ R for which the system of linear equations 2 x - y + 2 z = 2 x - 2 y…

Let S be the set of all λ∈R for which the system of linear equations

2x-y+2z=2

x-2y+λz=-4

x+λy+z=4

has no solution. Then the set S

  1. Contains more than two elements
  2. Is an empty set
  3. Is a singleton
  4. Contains exactly two elements

Solution

 For no solution Δ=0 and at least one of Δ1,Δ2,Δ3 is non-zero.
Δ=2-121-2λ1λ1=-λ-12λ+1
Δ1=2-12-4-2λ4λ1=-2λ2+6λ-4
Δ=0⇒  λ=1,-12

 And for  λ=1,-12,  ∆1≠0
Hence, S=1,-12

Asked in: JEE Main 2020 (02 Sep Shift 1)

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