Question

For 𝛼 , 𝛽 ∈ R, consider the system of linear equations
𝑥 + 𝑦 + 𝑧 = 1
3𝑥 + 𝑦 + 2𝑧 = 2
5x + 𝛼𝑦 + 𝛽𝑧 = 3
Then

• A. for every (𝛼, 𝛽 ) , 𝛼 = 𝛽, the system is consistent
• B. there exists (𝛼, 𝛽 ), satisfying 𝛼 − 2𝛽 + 5 = 0, for which the system has a unique solution
• C. there exists a unique pair (𝛼, 𝛽) for which the system has infinitely many solutions
• D. for every (𝛼, 𝛽), 𝛼 ≠ 𝛽, satisfying 𝛼 − 2𝛽 + 5 = 0, the system has infinitely many solutions

Answer 1

Answer: (C)

there exists a unique pair (𝛼, 𝛽) for which the system has infinitely many solutions

Answer 2

The correct option is (C): there exists a unique pair (𝛼, 𝛽) for which the system has infinitely many solutions