Results 1 to 3 of 3

Math Help - basis and dimension

  1. #1
    Newbie
    Joined
    Dec 2012
    From
    leb
    Posts
    9

    basis and dimension

    can you please help me with this problem I am a bit confused.If you could show me the steps it would be really helpful thank you.
    linear algebra | Flickr - Photo Sharing!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,392
    Thanks
    758

    Re: basis and dimension

    step one: convert all the matrices in S into vectors in R4.

    this turns S into span({(1,1,0,0),(2,2,0,0),(0,1,0,0),(1,2,0,0),(15, 1,0)}

    it should be obvious we can eliminate (2,2,0,0) from this set without fear, since it's just 2(1,1,0,0).

    also note that (1,2,0,0) = (1,1,0,0) + (0,1,0,0), so we don't need (1,2,0,0), either (it's a linear combination of the first two vectors).

    that leaves just 3 vectors left (1,1,0,0), (0,1,0,0) and (1,5,1,0). is this a linearly independent set?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2012
    From
    leb
    Posts
    9

    Re: basis and dimension

    thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Basis and dimension
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 4th 2010, 12:02 AM
  2. Basis and dimension
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 26th 2010, 07:43 AM
  3. Dimension and basis
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 17th 2009, 09:54 AM
  4. Dimension and basis
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 15th 2008, 09:17 AM
  5. Basis and Dimension
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 22nd 2007, 10:03 PM

Search Tags


/mathhelpforum @mathhelpforum