1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Subspace Theorem

  1. Oct 9, 2008 #1
    Use the subspace Theorem to decide if the following are subspaces of P2, the vector space of all polynomials of degree at most 2.

    a) R1 = {ao + a1x +a2x^2 | ao = 0}
    b) R1 = {ao + a1x +a2x^2 | a1 = 1}
    c) R1 = { p E P2 | p has exactly degree 2}

    (for part c 'E' is 'element of')


    a) Is a subspace, closed under vector addition and scalar multiplication

    b) Isn't a subspace, vector addition doesn't hold take (a,1,c) + (d,1,e) = (a+d,2,c+e)
    the value for a1 is 1 so its not a subspace.

    c) Isn't a subspace, take -x^2 and x^2 under addition they equal 0 and aren't degree 2.

    I'm unsure of part c whether i've just interpreted it wrongly or just made a mistake but for some reason i just doesn't feel right..

    any help would be appreciated as usual, thanks :)
  2. jcsd
  3. Oct 9, 2008 #2
    Everything is correct from my POV.
  4. Oct 10, 2008 #3


    User Avatar
    Science Advisor

    Point of grammar, not mathematics: "and aren't degree 2" implies that -x^2 and x^2 are not of degree 2 which is, of course, not true. You should have said "which isn't degree 2" making it clear that it is their sum, the 0 polynomial, which is not of degree 2.

  5. Oct 10, 2008 #4
    Makes sense, will keep it in mind for future reference so i don't get arrested for bad grammar ;)

    Love you!
  6. Oct 10, 2008 #5


    User Avatar
    Science Advisor

    You got a warning this time- next time a ticket!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook