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Consider the following system of equations αx + 2y + z = 1 2αx + 3y + z = 1 3x + αy + 2z = b For some α, β ∈ R when which of the following is NOT correct? (1) It has no solution if α = -1 and β ≠ 2 (2) It has a solution for all α ≠ -1 and β = 2 (3) It has no solution for α = 3 and for all β ≠ 2 (4) It has no solution for α = -1 and for all β ∈ R

1. It has no solution if α = -1 and β ≠ 2
2. It has a solution for all α ≠ -1 and β = 2
3. It has no solution for α = 3 and for all β ≠ 2
4. It has no solution for α = -1 and for all β ∈ R

Correct answer: It has no solution for α = 3 and for all β ≠ 2

Solution

Option C is incorrect because when α = 3, the system can still have solutions depending on the value of β. The conditions for no solution are not met in this case, making the statement false.

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