Results 1 to 2 of 2

Math Help - Spans

  1. #1
    sgc
    sgc is offline
    Newbie
    Joined
    Feb 2009
    Posts
    1

    Spans

    Prove that span ({x})= {ax: a in F} for any vector x in a vector space. Interpret this result geometrically in R^3.

    Now, I understand that the span of {x}= a1v1 + a2v2 + . . . anvn. But how does {ax} = a1v1+ a2v2+ . . . anvn? Unless I've got it all wrong.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121
    Quote Originally Posted by sgc View Post
    Prove that span ({x})= {ax: a in F} for any vector x in a vector space. Interpret this result geometrically in R^3.

    Now, I understand that the span of {x}= a1v1 + a2v2 + . . . anvn.'
    No, you don't understand that. That's not true because there is no "v1", "v2", ... "vn" in this problem. The span of a set of vectors is the set of all linear combinations of the vectors in that set. IF the set of vectors is {v1, v2, ..., v3} THEN the span is the set of vectors of the form a1v1+ a2v3+ ...+ anvn. But the span of a single vector {x} is the set of all multiples of x. What is that?

    But how does {ax} = a1v1+ a2v2+ . . . anvn? Unless I've got it all wrong.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Spans
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 25th 2010, 04:32 AM
  2. Help with spans
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: July 20th 2010, 05:47 AM
  3. Subspaces & spans
    Posted in the Advanced Algebra Forum
    Replies: 21
    Last Post: December 4th 2009, 09:53 AM
  4. Spans
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 5th 2009, 04:03 AM
  5. Basis/Spans
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: November 4th 2009, 11:22 PM

Search Tags


/mathhelpforum @mathhelpforum