1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

2 simple vector spaces question

  1. Apr 24, 2005 #1
    hi,i got 2 question about vector spaces :

    1. Do the set of all n-tuples of real numbers of the form (x, x1 ,x2.....xn) with the standard operation on R^2 are vector spaces?

    2.Do the set of all positive real numbers with operations

    x+y =x*y and kx=x^2 are vector space?
     
  2. jcsd
  3. Apr 24, 2005 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    1 makes no sense. What do "the standard operations of R^2", which are undefined, have to do with the n-tuples of real numbers? R^n is a vector space.

    2, just try and verify the axioms, or figure out where they may go wrong.
     
  4. Apr 24, 2005 #3
    those question is from a book ...........
     
  5. Apr 24, 2005 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    And does the book use phrases like "those question"?

    Once again: your first question makes no sense. It would make sense if you asked "Does the set of all n-tuples of real numbers of the form (x1 ,x2.....xn) with the standard operation on R^n form a vector space?". In that case the anser is obviously "yes". It makes no sense to talk about " real numbers of the form (x1 ,x2.....xn) with the standard operation on R^2" because you can't apply the operations on R^2 to R^n.

    The second question, "2.Is the set of all positive real numbers with operations
    x+y =x*y and kx=x^2 a vector space?" is reasonable. Matt Grimes' point was that it is just a matter of checking the axioms for (or definition of) a vector space.
     
  6. Apr 25, 2005 #5
    so you are saying that :
    the set of all positive real numbers with operations
    x+y =x*y and kx=x^2 are vector space?
     
  7. Apr 25, 2005 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    No, we are saying you should check to see if the "axioms" for a vector space are satisfied yourself. In particular, is the "distributive law", k(x+y)= kx+ ky, satisfied?
     
  8. Apr 26, 2005 #7
    ( a 1 ) --- is this 2x2 matrix a vector space ? sorry for asking this coz this is abstract
    1 b me
     
  9. Apr 27, 2005 #8

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Why is it abstract? What are the operations, for instance, what is k*M for some scalar k? Is that in the set? Check the rules, there really is nothing complicated or hidden in this:

    to check if S is a vector space over R, say, check the rules: is ks in S when s is in S and k is in R? ie if s satisfies the rules to be in S, does ks? Similarly what about s+t when s and t are in S? is there a zero vector? Just three simple rules to check.
     
  10. Apr 27, 2005 #9
    there are a few more rules to check too (like the afformentioned distributive property).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: 2 simple vector spaces question
  1. Vector space question (Replies: 8)

Loading...