Results 1 to 6 of 6

Math Help - How to prove vectors span a space?

  1. #1
    Newbie
    Joined
    Jun 2007
    Posts
    6

    How to prove vectors span a space?

    Hi,

    How would i prove that three given vectors span the space R^4?

    The vectors are as follows:

    a1= [ 0, 5,0,2 ]
    a2= [6,1,3,-1]
    a3= [1,4,4,3]

    Thanks,
    Carl
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,817
    Thanks
    316
    Awards
    1
    Quote Originally Posted by Carl505 View Post
    Hi,

    How would i prove that three given vectors span the space R^4?

    The vectors are as follows:

    a1= [ 0, 5,0,2 ]
    a2= [6,1,3,-1]
    a3= [1,4,4,3]

    Thanks,
    Carl
    They don't. \mathbb{R} ^4 requires at least 4 vectors to span it.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2007
    Posts
    6
    There is another problem in my textbook that gives three different vectors and states that the subspace of R^4 is spanned by the given vectors, and then it asks to show that theses vectors form the a basis for V (which is the subspace)

    So does that mean that they are not a basis for the subspace because they do not span the the subspace? But then again, the problem states that the space is spanned by the vectors.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    There is a difference in spanning a space such as R^4 and spanning a subspace of that space. If you can show that the three given vectors are linearly independent then those three vectors span a 3-dimensional subspace of R^4.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jun 2007
    Posts
    6
    Ok that makes sense...Thanks!

    one more question though,

    Can you show the linear indepence by finding the row reduced echelon form of the matrix with the three vectors. And then if they have leading ones in the columns, that would conclude that they are linear independent.

    Or is there another way of showing their linear independence?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    Quote Originally Posted by Carl505 View Post
    Can you show the linear indepence by finding the row reduced echelon form of the matrix with the three vectors.
    Yes, count the nonzero rows.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How do I determine which space these vectors span?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 4th 2010, 03:44 PM
  2. Prove that span{x,y}=span{y,z}
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: September 24th 2010, 05:17 AM
  3. Do the 3 vectors span the space? Check :)
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: July 17th 2010, 04:53 AM
  4. Span of a vector space
    Posted in the Advanced Algebra Forum
    Replies: 10
    Last Post: August 25th 2009, 03:13 AM
  5. need help...about vector space and span
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 18th 2008, 09:35 PM

Search Tags


/mathhelpforum @mathhelpforum