Question:

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

IIT JAM EN - 2023
IIT JAM EN

Updated On: Oct 1, 2024

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

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The Correct Option is C

Solution and Explanation

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

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

The Correct Option is C

Solution and Explanation

Top Questions on Linear Algebra

Questions Asked in IIT JAM EN exam

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