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JEE Main20202 Sep 2020Morning ShiftMathematicsDeterminantsActual

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 + λ z = - 4 x + λ y + z = 4 has no solution. Then the set S

Options

  1. AContains more than two elements
  2. BIs an empty set
  3. CIs a singleton
  4. DContains exactly two elements

Correct answer

D. Contains exactly two elements

Step-by-step solution

For no solution Δ = 0 and at least one of Δ 1 , Δ 2 , Δ 3 is non-zero. Δ = 2 - 1 2 1 - 2 λ 1 λ 1 = - λ - 1 2 λ + 1 Δ 1 = 2 - 1 2 - 4 - 2 λ 4 λ 1 = - 2 λ 2 + 6 λ - 4 Δ = 0 ⇒    λ = 1 , - 1 2 And for λ = 1 , - 1 2 ,     ∆ 1 ≠ 0 Hence, S = 1 , - 1 2

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