Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By HallsofIvy

Math Help - Dimensions of linear subspaces

  1. #1
    Junior Member
    Joined
    Nov 2013
    From
    Germany
    Posts
    40
    Thanks
    1

    Dimensions of linear subspaces



    i) 2 Dimensions

    (1,0,0,0) * 8 = (8,0,0,0)
    (1,0,0,0) * 15=(15,0,0,0)

    ii) 1 Dimension because I have one vector only? Abb (N,R) means f:N-->R

    iii) Dont know. How do I start here? I have modulo 3, but thats all. How do I find out the dimension here?

    iv) 2 Dimensions
    (1,1,0) + (0,0,1) = (1,1,1)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,405
    Thanks
    1328

    Re: Dimensions of linear subspaces

    (i) fairly obviously has dimension 1, not 2. Was that a typo? As for (ii), in what sense is {(1, 2, 3, 4, ...)} a function from N to R?

    For (iii), Are the two vectors independent? That is, is one a multiple of the other? Certainly 2*\overline{1}= \overline{2}. Is 2*\overline{2}= \overline{1}?
    Thanks from Cyganek
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2013
    From
    Germany
    Posts
    40
    Thanks
    1

    Re: Dimensions of linear subspaces

    i) oh yea sorry it was a typo indeed.

    ii) Well the span is a subset of the function that goes from N to R. Dont know more than this

    iii) Well 2*1 = 2 and 2*2 = 1. But I cant tell why you do 2*2 in the first place and how to get a conclusion from this?
    Additionally 1+2 = 0 and 2+1 = 0. This would mean its linear dependant, right? But does this help? Im just throwing out my thoughts here.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,405
    Thanks
    1328

    Re: Dimensions of linear subspaces

    Quote Originally Posted by Cyganek View Post
    i) oh yea sorry it was a typo indeed.

    ii) Well the span is a subset of the function that goes from N to R. Dont know more than this
    That makes no sense. The "span" is a vector space, not a function.

    iii) Well 2*1 = 2 and 2*2 = 1. But I cant tell why you do 2*2 in the first place and how to get a conclusion from this?
    Additionally 1+2 = 0 and 2+1 = 0. This would mean its linear dependant, right? But does this help? Im just throwing out my thoughts here.
    That is the whole point. Yes, [latex]2(\overline{1}, \overline{0}, \overline{2})= (\overline{2}, \overline{0}, \overtime{1})[/latex] so one is a multiple of the other- they are dependent. That is equivalent to just one of the two vectors so this span is one dimensional.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. need help proving a statment with subspaces dimensions
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: January 14th 2013, 06:39 PM
  2. Tricky question, subspaces dimensions
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: January 6th 2013, 12:40 PM
  3. Dimensions of the Four Subspaces
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: February 13th 2011, 09:22 AM
  4. question on subspaces and dimensions
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 13th 2010, 10:54 AM
  5. Dimensions and Subspaces Help
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 18th 2008, 03:23 AM

Search Tags


/mathhelpforum @mathhelpforum