Exterior Algebra Quiz
8 Questions
1 Views

Exterior Algebra Quiz

Created by
@ProsperousNavy

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is an element of $\wedge ^{k}V$ called?

  • Scalar product
  • Vector sum
  • k-blade (correct)
  • Multivector sum

    • What does the expression $v\wedge v$ equal to for all $v \in V$?

  • 0 (correct)
  • 1
  • $-v$
  • v

    • What is the exterior algebra of a vector space V denoted as?

  • $\wedge V$ (correct)
  • $\wedge ^{3}V$
  • $\wedge ^{k}V$
  • $\wedge ^{2}V$

    • What property does the exterior product $\wedge$ satisfy?

    <p>Alternating property</p> Signup and view all the answers

    What is the name given to elements in $\wedge kV$?

    <p>k-multivectors</p> Signup and view all the answers

    What is the result of rotating a point (x, y) by an angle θ counterclockwise about the origin?

    <p>(x<em>cos(θ) - y</em>sin(θ), x<em>sin(θ) + y</em>cos(θ))</p> Signup and view all the answers

    What is the effect of rotating a vector v by an angle θ using a 2x2 rotation matrix R?

    <p>Rv</p> Signup and view all the answers

    What is the determinant of a 2x2 rotation matrix R?

    <p>1</p> Signup and view all the answers

    More Like This

    Exterior Inspections
    3 questions

    Exterior Inspections

    KidFriendlyOstrich avatar
    KidFriendlyOstrich
    Exterior Building Maintenance Quiz
    5 questions

    Exterior Building Maintenance Quiz

    AwestruckToad avatar
    AwestruckToad
    Exterior Algebra and Wedge Product Quiz
    10 questions

    Exterior Algebra and Wedge Product Quiz

    ReputableLogic avatar
    ReputableLogic
    Exterior Algebra Quiz
    5 questions

    Exterior Algebra Quiz

    StraightforwardNavy avatar
    StraightforwardNavy
    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser