Let be a subspace of a vector space . Then which of the following sets of vectors forms a basis of ?
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1 mark, −0.333MathematicsVector spaces, rank and eigenvaluesLinear independence, span and basisModerateabout 2 min
IIT JAM 2022 Question 6: Vector spaces, rank and eigenvalues
Answer and worked solution
Answer: MTA
In the exam this question was dropped and every candidate received the marks.
For context: any basis of a subspace of must be linearly independent, so the four-vector set in (B) cannot be a basis. A single-answer MCQ requires exactly one option to be a valid basis; the printed options (in particular the two-vector set) do not resolve cleanly, which is why every attempt was credited.
Plain-text version
Let W be a subspace of a vector space ℝ³. Then which of the following sets of vectors forms a basis of W? (A) (1, 2, 1) and (1, -2, 5) (B) (1, 3, 2), (1, -1, 0), (4, -1, 0) and (3, 1, -3) (C) (1, 1, 1), (1, 2, 3) and (2, -1, 1) (D) (1, -2, 1), (2, 1, -1) and (7, -4, 1)
Also written as: Let W be a subspace of a vector space R^3. Then which of the following sets of vectors forms a basis of W?
Vector spaces, rank and eigenvalues has come up 41 times in 6 exams since 2008.
What this question tests
This question is on Linear independence, span and basis, part of Vector spaces, rank and eigenvalues in Mathematics.
Whether vectors depend on each other, what they span and when they form a basis.
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Question from the IIT JAM 2022 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.