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JEE Main2016MathematicsDeterminantsActual

The system of linear equations x + λ y - z = 0 λ x - y - z = 0 x + y - λ z = 0 has a non -trivial solution for

Options

  1. AExactly two values of λ
  2. BExactly three values of λ
  3. CInfinitely many values of λ
  4. DExactly one value of λ

Correct answer

B. Exactly three values of λ

Step-by-step solution

For non - trivial solution. Δ = 1 λ - 1 λ - 1 - 1 1 1 - λ = 0 1 λ + 1 - λ - λ 2 + 1 - 1 λ + 1 = 0 λ + 1 - λ 1 - λ 1 + λ - λ + 1 = 0 λ 1 - λ 1 + λ = 0 λ = 0 , λ = 1 , λ = - 1 Exactly there value of λ .

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