Results 1 to 4 of 4

Math Help - Linearility/spanning sets.

  1. #1
    Junior Member
    Joined
    Oct 2010
    Posts
    71

    Linearility/spanning sets.

    Let {x1, x2... xn} be a spanning set for V.

    If we add an additional vector xn+1 to the set , will we still have a spanning set?



    I'm struggling to understand linear span. I know that if x1, x2.. xn is a spanning set for V, then it takes all the linear combinations of c1x1, c2x2.. cnxn.

    I don't see how this extra vector affects it though?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    http://www.mathhelpforum.com/math-he...es-144330.html

    2nd post proves both cases: n+1 is in the span and n+1 isn't in the span
    Last edited by dwsmith; December 9th 2010 at 02:09 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2010
    Posts
    71
    Quote Originally Posted by dwsmith View Post
    http://www.mathhelpforum.com/math-he...es-144330.html

    2nd post proves both cases: n+1 is in the span and n+1 isn't in the span
    Thanks alot!

    You were of great help
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,790
    Thanks
    1531
    Quote Originally Posted by chr91 View Post
    Let {x1, x2... xn} be a spanning set for V.

    If we add an additional vector xn+1 to the set , will we still have a spanning set?



    I'm struggling to understand linear span. I know that if x1, x2.. xn is a spanning set for V, then it takes all the linear combinations of c1x1, c2x2.. cnxn.
    Phrased that way, it seems backwards. The point is not that all linear combinations are in V but that every vector in V is such a linear combination.

    I don't see how this extra vector affects it though?
    It doesn't affect it! That's the whole point. If x1, x2, ..., xn is a spanning set for V, then any vector u in V can be written as a linear combination of them: u= a1x1+ a2x+ 2+ ...+ anxn, and any one of the "a"s can be 0. If put in an additional xn+1, just think of it as always having coefficient 0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Spanning Sets
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: October 28th 2010, 04:31 PM
  2. spanning sets
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 10th 2010, 07:46 PM
  3. Spanning sets?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 15th 2009, 07:44 PM
  4. spanning sets
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 14th 2008, 04:14 AM
  5. Spanning sets for R^3
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: April 29th 2008, 12:54 PM

Search Tags


/mathhelpforum @mathhelpforum