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Consider the system of equations x + 2 y + 3 z = 6, 4 x + 5 y + 6 z = λ, 7 x + 8 y + 9 z = 24. Then, the value of λ for which the system has infinite solutions is

Options

  1. A15
  2. B20
  3. C16
  4. D30

Correct answer

A. 15

Step-by-step solution

Note that D = 1 2 3 4 5 6 7 8 9 = 0 R 3 → R 3 - 2 R 2 + R 1 D 1 = 6 2 3 λ 5 6 24 8 9 = - 3 30 - 2 λ D 2 = 1 6 3 4 λ 6 7 24 9 = 6 30 - 2 λ D 3 = 1 2 6 4 5 λ 7 8 24 = - 3 30 - 2 λ Hence, for λ = 15 the system has infinite solutions

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