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 2013 › Q25
2 marksMathematics › Vector spaces, rank and eigenvalues › Linear maps, rank and projectionsEasyabout 1 min

DSE 2013 Question 25: Vector spaces, rank and eigenvalues

Consider f:ℜ2→ℜ3f:\Re^2\to\Re^3f:ℜ2→ℜ3 defined by f(x,y)=(x+2y, x−y, −2x+3y)f(x,y)=(x+2y,\,x-y,\,-2x+3y)f(x,y)=(x+2y,x−y,−2x+3y), and g:ℜ2→ℜ2g:\Re^2\to\Re^2g:ℜ2→ℜ2 defined by g(x,y)=(x+1, y+2)g(x,y)=(x+1,\,y+2)g(x,y)=(x+1,y+2). Then:

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

Consider f:ℜ²→ℜ³ defined by f(x,y)=(x+2y, x-y, -2x+3y), and g:ℜ²→ℜ² defined by g(x,y)=(x+1, y+2). Then: (A) Both f and g are linear transformations. (B) f is a linear transformation, but g is not. (C) f is not a linear transformation, but g is. (D) Neither f nor g is a linear transformation.

Also written as: Consider f: Re^2-> Re^3 defined by f(x,y)=(x+2y, x-y, -2x+3y), and g: Re^2-> Re^2 defined by g(x,y)=(x+1, y+2). Then:

Vector spaces, rank and eigenvalues has come up 41 times in 6 exams since 2008.

What this question tests

This question is on Linear maps, rank and projections, part of Vector spaces, rank and eigenvalues in Mathematics.

Linear transformations, their range and rank, and projection operators.

TestStop has 14 past-paper questions on this subtopic.

Practise Vector spaces, rank and eigenvaluesMore on Linear maps, rank and projections

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…
  • 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?

Question from the DSE 2013 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.