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!

More on vector spaces

  1. Feb 21, 2006 #1
    Determine if this is a vector space with the indicated operations

    the set of V of all polynominals of degree >=3, togehter iwth 0, operations of P (P the set of polynomials)

    now all the scalar multiplication axioms hold.
    the text however says that the axion
    [tex] \mbox{For u,v} \in V, \mbox{then} \ u+v \in V [/tex] does not hold

    well ok take two polynomials
    [tex] u(x) = a_{3} x^3 + ... + a_{n} x^n [/tex]
    [tex] v(x) = b_{3} x^3 + ... + b_{k} x^k [/tex]
    where both n,k>= 3, then suppose k< n
    [tex] u(x) + v(x) = (a_{3} + b_{3}) x^3 + ... + (a_{k} + b_{k}) x^k + ... + a_{n} x^n [/tex]
    which is certainly a polynomial or degree >= 3 isnt it?
    It also applies for n<k and n = k
    is the text book wrong?
  2. jcsd
  3. Feb 21, 2006 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    What is the degree of the following poly


    now, do you see your error?
  4. Feb 21, 2006 #3
    ok let me correct that then
    n,k >= 3
    [tex] u(x) = a_{0} + a_{1} x + ... + a_{n} x^n [/tex]
    [tex] v(x) = b_{0} + b_{1} x + ... + b_{k} x^k [/tex]
    then for n< k
    [tex] u + v = (a_{0} + b_{0}) + ... + (a_{k} + b_{k}) x^k + ... + a_{n} x^n [/tex]

    stil lseems to be of degree three to me
    however if k=n and an= -bn then the polynomial is no more degree 3
    is this corret?
  5. Feb 21, 2006 #4

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Why don't you just find a counter example? two polys of degree 3 or greaterwhose sum isn't? A single counter examplem suffices.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: More on vector spaces
  1. Vector space (Replies: 8)

  2. Vector Space (Replies: 3)

  3. Not a Vector Space (Replies: 3)

  4. Vector Space (Replies: 10)