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Consider the system of linear equations x + y + z = 5, x + 2y + λ²z = 9, x + 3y + λz = 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

Solution

The correct option states that the system has a unique solution when λ is not equal to 1 and μ is not equal to 13, which is true because under these conditions, the equations are independent and can be solved for a single set of values for x, y, and z.

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