Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

fleauworld

  • 4 years ago

Let Z denote the set of all integers with addition defined in the usual way, and define scalar multiplication, denoted o, by: alpha o k = [[alpha]].k for all k in Z where [[alpha]] denotes the greatest integer less than or equal to alpha, for example, 2.25 o 4 = [[2.25]].4 =2..4 = 8 show that Z, together with these operations, is not a vector space. Which axioms fail to hold?

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

    Distributivity of scalar multiplication with respect to field addition (a + b)v = av + bv Compatibility of scalar multiplication with field multiplication a(bv) = (ab)v

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

    I agree with the second answer, but why the Distributivity of scalar multiplication with respect to field addition fail to hold ?

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

    straight out of wikipedia Distributivity of scalar multiplication with respect to field addition (a + b)v = av + bv let a=2.5 and b=3.5

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

    oh I see never mind, thx :)

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

    let them better be a=2,5 and b=3,6

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

    what was ur approach to finding the solutions please ? did you test for all axioms one by one ?

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

    not really, becouse all the rest are not afected by any weird definition. Just this two

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

    the other one also seem to work Compatibility of scalar multiplication with field multiplication a(bv) = (ab)v a=4 and b=2.5

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

    hum ok I see, thank you mate

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

    you have to choose two numbers where decimal part sum is bigger than 1

  11. 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