Skip to content
We use only essential cookies to keep you signed in and remember your preferences. See our Cookie Policy.
TestStop
MocksPracticeResourcesIndiaBlogPricing
Sign in
Questions › DSE › DSE 2014 › Q23
2 marks, −0.666666666666667Mathematics › Vector spaces, rank and eigenvalues › Linear independence, span and basisModerateabout 2 min

DSE 2014 Question 23: Vector spaces, rank and eigenvalues

Suppose A1,A2,…A_1,A_2,\dotsA1​,A2​,… is a countably infinite family of subsets of a vector space, all linearly independent, with A1⊆A2⊆⋯A_1\subseteq A_2\subseteq\cdotsA1​⊆A2​⊆⋯. Then ⋃i=1∞Ai\bigcup_{i=1}^\infty A_i⋃i=1∞​Ai​ is

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

Suppose A₁,A₂,… is a countably infinite family of subsets of a vector space, all linearly independent, with A₁⊆ A₂⊆⋯. Then ⋃ᵢ₌₁^∞ Aᵢ is (A) a linearly independent set of vectors (B) a linearly dependent set of vectors (C) linearly independent provided the vectors are orthogonal (D) not necessarily either dependent or independent

Also written as: Suppose A_1,A_2,... is a countably infinite family of subsets of a vector space, all linearly independent, with A_1 subseteq A_2 subseteq.... Then union_(i=1)^(inf) A_i is

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.

TestStop has 13 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2021 · Q20Let W be the subspace of ℝ³ spanned by (0, -1, 2) and (2, -1, 0). Which one of the following vectors lies in…
  • IIT JAM 2022 · Q6Let W be a subspace of a vector space ℝ³. Then which of the following sets of vectors forms a basis of W?
Practise Vector spaces, rank and eigenvaluesMore on Linear independence, span and basis

Similar questions from other papers

  • IIT JAM 2024 · Q37Let M = [α -6; -1 1], α ∈ R. If the eigenvalues of M are β and 4, which of the following is/are CORRECT?
  • CUET-PG 2023 Shift 2 · Q67Find the scalars λ₁ and λ₂ that are attached to v = [1; 2] and w = [3; 1] to yield [1; 0]
  • IIT JAM 2023 · Q35For α,β∈ℝ, α≠β, if -2 and 5 are eigenvalues of M=[1-α 1+β; β α+β] and X=[x₁,x₂]ᵀ is an eigenvector for -2, then
  • UGC-NET 2023 · Q60Consider a matrix A = [[3, 5],[-2, -4]]. Consider the following statements on the characteristic polynomial, Eigenvalues and Eigenvectors. (A) The characteristic…

Question from the DSE 2014 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.