Results 1 to 4 of 4

Math Help - Span (Lin Alg)

  1. #1
    Member
    Joined
    Sep 2006
    Posts
    221

    Span (Lin Alg)

    Given the following vectors:

    v_1 = [1, -2, 3]

    v_2 = [-1, 1, 0]

    v_3 = [1, -3, 5]

    Find a vector w in R^3 (which is not a scalar multiple of v_1, v_2, or v_3) that's in the Span{v_1, v_2, v_3} but not in the Span{v_1, v_2}.

    .
    .
    .
    Not sure. Is it asking me to find an augmented vector so when I row reduce the 3x4 matrix it's consistent, but when I take that same vector and augment it with v_1, v_2 (so I'd have a 2x4 matrix) it's not consistent? Not sure...
    Last edited by Ideasman; October 1st 2007 at 06:45 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Sep 2006
    Posts
    221
    Can anyone point me in the right direction?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,925
    Thanks
    332
    Awards
    1
    Quote Originally Posted by Ideasman View Post
    Given the following vectors:

    v_1 = [1, -2, 3]

    v_2 = [-1, 1, 0]

    v_3 = [1, -3, 5]

    Find a vector w in R^3 (which is not a scalar multiple of v_1, v_2, or v_3) that's in the Span{v_1, v_2, v_3} but not in the Span{v_1, v_2}.
    I haven't bothered to show it but visually it looks like your 3 vectors span \mathbb{R} ^3, so essentially the question is asking for a vector in \mathbb{R} ^3 that is not in the plane formed by \text{Span} \{ v_1, v_2 \} . ie. find a vector perpendicular to the plane formed by v_1, v_2.

    (Of course, you need to write this vector in terms of your basis.)

    -Dan
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Sep 2006
    Posts
    221
    Quote Originally Posted by topsquark View Post
    I haven't bothered to show it but visually it looks like your 3 vectors span \mathbb{R} ^3, so essentially the question is asking for a vector in \mathbb{R} ^3 that is not in the plane formed by \text{Span} \{ v_1, v_2 \} . ie. find a vector perpendicular to the plane formed by v_1, v_2.

    (Of course, you need to write this vector in terms of your basis.)

    -Dan
    I'm going crazy!

    I confirmed that v_1, v_2, v_3 do span R^3.

    Wouldn't ANY vector work, mean we have 2 vectors, and if we AUGMENT it with a 3rd, it will ALWAYS be inconsistent...but if we augment it with the matrix we already know spans R^3, wouldn't ANY vector work for my question...grrr confusing.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove that span{x,y}=span{y,z}
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: September 24th 2010, 05:17 AM
  2. Span help
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: July 20th 2010, 07:43 PM
  3. Span of R^3
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 22nd 2010, 08:37 PM
  4. Proving span{v1,v2,..} = span{w1, w2, ...w3}
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 4th 2010, 11:35 AM
  5. Span of a Set
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 29th 2006, 12:51 PM

Search Tags


/mathhelpforum @mathhelpforum