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Consider the system of linear equations x + y + z = 5, x + 2y + λ 2 z = 9, x + 3y + λ z = μ , where λ , μ ∈ R. Then, which of the following statement is NOT correct?

1. System has unique solution if λ ≠ 1 and μ ≠ 13
2. System is inconsistent if λ = 1 and μ ≠ 13
3. System has infinite number of solutions if λ = 1 and μ = 13
4. System is consistent if λ ≠ 1 and μ = 13

Correct answer: System has unique solution if λ ≠ 1 and μ ≠ 13

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