Results 1 to 3 of 3

Math Help - Vector Space

  1. #1
    Junior Member
    Joined
    Aug 2008
    Posts
    35

    Vector Space

    I'd like to know how I can prove "the set of all vectors V = [v_1, v_2, v_3, v_4] R^4 with v_1+v_2=0 and v_3-v_4 = 1" that it is vector space or not?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    Not really the right place for that kind of algebra.

    Look through your book. There is a numbered list of requirements to be a Vector Space. Find it and prove it - one requirement at a time.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,775
    Thanks
    1514
    Quote Originally Posted by noppawit View Post
    I'd like to know how I can prove "the set of all vectors V = [v_1, v_2, v_3, v_4] R^4 with v_1+v_2=0 and v_3-v_4 = 1" that it is vector space or not?
    By using the definition of vector space. But since you are already given that this is a set of vectors, you know that things like "associative law", etc. are true. What you need to do is see if, given that v_1+ v_2= 0, [tex]v_3- v_4= 1[/itex], u_1+ u_2= 0, and u_3- u_4= 1 then the same is true of the sum [v_1, v_2, v_3, v_4]+ [u_1, u_2, u_3, u_4]= [v_1+u_1, v_2+ u2, v_3+ u_3, v_4+u_4]. That is, is (v_1+ u_1)+ (v_2+ u_2)= 0 and (v_3+ u_3)- (v_4+ u_4)= 1. I recommend you look closely at that last equation!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Dual Space of a Vector Space Question
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 16th 2011, 03:02 AM
  2. Replies: 2
    Last Post: April 1st 2011, 02:40 AM
  3. Banach space with infinite vector space basis?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: March 24th 2011, 06:23 PM
  4. Replies: 15
    Last Post: July 23rd 2010, 11:46 AM
  5. Isomorphism beetwenn vector space and sub space
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 30th 2008, 10:05 AM

Search Tags


/mathhelpforum @mathhelpforum