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JEE Main202118 Mar 2021Evening ShiftMathematicsDeterminantsActual

Let the system of linear equations 4 x + λ y + 2 z = 0 2 x - y + z = 0 μ x + 2 y + 3 z = 0 , λ , μ ∈ R has a non-trivial solution. Then which of the following is true?

Options

  1. Aμ = 6 ,   λ ∈ R
  2. Bλ = 2 ,   μ ∈ R
  3. Cλ = 3 ,   μ ∈ R
  4. Dμ = - 6 ,   λ ∈ R

Correct answer

A. μ = 6 ,   λ ∈ R

Step-by-step solution

For non-trivial solution 4 λ 2 2 - 1 1 μ 2 3 = 0 ⇒ - 20 - 6 λ + λ μ + 8 + 2 μ = 0 ⇒ 2 μ - 6 λ + λ μ = 12 when μ = 6 ,   12 - 6 λ + 6 λ = 12 which is satisfied by all λ When λ = 2 ,   4 μ = 24 When λ = 3 ,   5 μ = 30 When μ = - 6 ,   - 12 - 6 λ - 6 λ = 12

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