A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

can someone help explain how to determine if something is a vector space or not

  • This Question is Closed
  1. Zarkon
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    http://en.wikipedia.org/wiki/Vector_space#Definition

  2. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you have to check it for the axioms and see if they are true or not

  3. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how do you use the axioms to determine for instance if the set of all fifth degree polynomials with the standard operations is a vestor space

  4. Zarkon
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Is that space closed under addition

  5. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i guess there is a subtlety here. if it means the polynomial must have degree 5, then there is no zero vector. if it means degree 5 or less, then yes

  6. Zarkon
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    right...as stated it is not a vector space...no zero vector and no closure of addition

  7. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that is the very thing that Im confused about how do you determine that there is no zero vector and no closure of addition

  8. Zarkon
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the zero vector has to be just the number 0 0 is not a 5th degree polynomial

  9. Zarkon
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[(x^5+3x)+(-x^5+x^2)=3x-x^2\] which is not a 5th degree polly

  10. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is there a vector (fifth degree polynomial in this case) say \[p(x)\] with \[p(x)+v(x)=v(x)\] for all fifth degree polynomials v the answer is no, because the only polynomial that would work would be the zero polynomial, which does not have degree 5

  11. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    further more, \[x^5-2x+(-x^5)\] does not have degree 5, so it is not closed under addition

  12. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what zarkon said

  13. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok that makes sense so what is the differance in saying it has fifth degree and fifth degree or less

  14. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is one a vector and one is not and why

  15. Zarkon
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    5th degree or less is a vector space

  16. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so what is the step by step method to determing the answer to these types of problems. I mean when talking about continuous functions and things like that wouldnt get a little tricky

  17. Zarkon
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    use the difinition I provided in my first post

  18. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i know it has to adhere to the list of axioms but can you explain it a little.

  19. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.