Results 1 to 2 of 2

Math Help - Vector Spaces

  1. #1
    Senior Member Danneedshelp's Avatar
    Joined
    Apr 2009
    Posts
    303

    Vector Spaces

    Hey,

    I am having trouble seeing why the following is not a vector space.

    "The set of all first-degree polynomial functions ax+b, a\neq0, whose graphs pass through the origin with the standard operations"

    By #4 " V has a zero vector 0 such that for ever u in V, u+0=u"

    I am not seeing why #4 keeps the above from being a vector space. I don't think I am understanding the zero vector as I should.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by Danneedshelp View Post
    Hey,

    I am having trouble seeing why the following is not a vector space.

    "The set of all first-degree polynomial functions ax+b, a\neq0, whose graphs pass through the origin with the standard operations"

    By #4 " V has a zero vector 0 such that for ever u in V, u+0=u"

    I am not seeing why #4 keeps the above from being a vector space. I don't think I am understanding the zero vector as I should.

    Thanks
    #4 fails because \mathbf{0}\notin V (pay attention to the condition a\neq0 and the fact that each of them go through the origin, implying b=0). If we didn't have the condition a\neq 0, then it would be a vector space because the zero vector would exist.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Is the intersection of two vector spaces a vector space?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 10th 2011, 12:55 PM
  2. [SOLVED] Vector Spaces
    Posted in the Advanced Algebra Forum
    Replies: 14
    Last Post: July 6th 2011, 10:58 AM
  3. Vector Spaces
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 27th 2010, 11:50 AM
  4. Replies: 3
    Last Post: June 1st 2008, 02:51 PM
  5. vector spaces help
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 22nd 2007, 07:58 AM

Search Tags


/mathhelpforum @mathhelpforum