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JEE Main20204 Sep 2020Evening ShiftMathematicsDeterminantsActual

If the system of equations x + y + z = 2 2 x + 4 y - z = 6 3 x + 2 y + λ z = μ has infinitely many solutions, then :

Options

  1. A  λ + 2 μ = 14
  2. B2 λ - μ = 5
  3. Cλ - 2 μ = - 5
  4. D2 λ + μ = 14

Correct answer

D. 2 λ + μ = 14

Step-by-step solution

For infinitely many solutions, all determinants should be zero. D = 1 1 1 2 4 - 1 3 2 λ = 0 ⇒ λ = 9 2 D 3 = 1 1 2 2 4 6 3 2 μ = 0 ⇒ μ = 5 Now check each option

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