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Consider the system of linear equation x + y + z = 4 μ , x + 2y + 2 λ z = 10 μ , x + 3y + 4 λ 2 z = μ 2 + 15, where λ , μ ∈ R . Which one of the following statements is NOT correct?

1. The system has infinite number of solutions if λ = 2 1 and μ = 15
2. The system is consistent if λ ≠ 2 1
3. The system is inconsistent if λ = 2 1 and μ ≠ 1
4. The system has unique solution if λ ≠ 2 1 and μ ≠ 1, 15

Correct answer: The system is inconsistent if λ = 2 1 and μ ≠ 1

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