Results 1 to 2 of 2

Math Help - Help with proof

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    146

    Help with proof

    This is a simple proof, and it makes sense logically, but I don't know how to show it. Any tips on how to prove stuff like this?

    if V is a vector space with basis {v1,...,vn} and W is a subspace of V = sp(v3,..,vn)
    show that if w E W and w = r1v1 + r2v2 for r1,r2 E R, then w = 0.

    Well since V has a basis of v1...vn, that means that sp(v1...vn) = V.
    All vectors in W can be written by a linear combination of v3...vn, thus if w is a linear combination of v1 and v2, and lies in W, that implies that it is the zero vector.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,517
    Thanks
    771

    Re: Help with proof

    Quote Originally Posted by Kuma View Post
    All vectors in W can be written by a linear combination of v3...vn, thus if w is a linear combination of v1 and v2, and lies in W, that implies that it is the zero vector.
    Yes, but how exactly is this implied? If w=r_1v_1+r_2v_2=r_3v_3+\dots+r_nv_n, then -r_1v_1-r_2v_2+r_3v_3+\dots+r_nv_n=0, so...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 15
    Last Post: June 8th 2011, 11:13 AM
  2. Replies: 5
    Last Post: October 19th 2010, 10:50 AM
  3. [SOLVED] direct proof and proof by contradiction
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 27th 2010, 10:07 PM
  4. Proof with algebra, and proof by induction (problems)
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: June 8th 2008, 01:20 PM
  5. proof that the proof that .999_ = 1 is not a proof (version)
    Posted in the Advanced Applied Math Forum
    Replies: 4
    Last Post: April 14th 2008, 04:07 PM

Search Tags


/mathhelpforum @mathhelpforum