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2 marks, −0.667MathematicsMatrices, determinants and linear systemsConsistency, rank and solution spacesHardabout 3 min
IIT JAM 2023 Question 20: Matrices, determinants and linear systems
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Plain-text version
For α,β∈ℝ, consider x+y+z=1, 3x+y+2z=2, 5x+α y+β z=3. Then (A) for every (α,β) with α=β, the system is consistent (B) there exists (α,β) with 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, with α-2β+5=0, the system has infinitely many solutions
Also written as: For alpha,beta in R, consider x+y+z=1, 3x+y+2z=2, 5x+alpha y+beta z=3. Then
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What this question tests
This question is on Consistency, rank and solution spaces, part of Matrices, determinants and linear systems in Mathematics.
Whether a system has no solution, one or many, and the shape of its solution set.
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