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 › Q2
1 mark, −0.333333333333333Mathematics › Vector spaces, rank and eigenvalues › Linear independence, span and basisModerateabout 2 min

DSE 2014 Question 2: Vector spaces, rank and eigenvalues

Let M=(4779)M=\begin{pmatrix}4&7\\7&9\end{pmatrix}M=(47​79​), A=(1111)A=\begin{pmatrix}1&1\\1&1\end{pmatrix}A=(11​11​), B=(1234)B=\begin{pmatrix}1&2\\3&4\end{pmatrix}B=(13​24​), C=(1145)C=\begin{pmatrix}1&1\\4&5\end{pmatrix}C=(14​15​). Then M=xA+yB+zCM=xA+yB+zCM=xA+yB+zC,

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

Let M=[4 7; 7 9], A=[1 1; 1 1], B=[1 2; 3 4], C=[1 1; 4 5]. Then M=xA+yB+zC, (A) but x,y,z are not unique (B) z=-1 (C) z=-1 and z=-2 both can hold (D) x,y,z are unique but z=2

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.