Results 1 to 7 of 7
Like Tree1Thanks
  • 1 Post By Walagaster

Thread: Proving that a subset of R^3 is a subspace (or not), and proof critique.

  1. #1
    Junior Member
    Joined
    Sep 2017
    From
    Astral Plane
    Posts
    61

    Proving that a subset of R^3 is a subspace (or not), and proof critique.

    (1) For each of the following subsets of R^3, prove that it is a subspace or prove that it is not a subspace.

    https://imgur.com/a/WIfqmDj

    Did I get it right?

    I'm especially concerned with the first part, I don't think I did that right..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Walagaster's Avatar
    Joined
    Apr 2018
    From
    Tempe, AZ
    Posts
    132
    Thanks
    63

    Re: Proving that a subset of R^3 is a subspace (or not), and proof critique.

    You are making the first part too hard. The zero vector [0,0,0] is trivially of the form [0,x,y]. It has nothing to do with A. The rest looks OK.
    Thanks from MrJank
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2017
    From
    Astral Plane
    Posts
    61

    Re: Proving that a subset of R^3 is a subspace (or not), and proof critique.

    So, though unnecessary, is that the first part correct?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member Walagaster's Avatar
    Joined
    Apr 2018
    From
    Tempe, AZ
    Posts
    132
    Thanks
    63

    Re: Proving that a subset of R^3 is a subspace (or not), and proof critique.

    Quote Originally Posted by MrJank View Post
    So, though unnecessary, is that the first part correct?
    No. I would not give credit for that argument because it misses the point.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Sep 2017
    From
    Astral Plane
    Posts
    61

    Re: Proving that a subset of R^3 is a subspace (or not), and proof critique.

    Quote Originally Posted by Walagaster View Post
    No. I would not give credit for that argument because it misses the point.
    Ok, I'm confused how to write it then. Would I just take a vector x from the subset and make its elements = to zero?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member Walagaster's Avatar
    Joined
    Apr 2018
    From
    Tempe, AZ
    Posts
    132
    Thanks
    63

    Re: Proving that a subset of R^3 is a subspace (or not), and proof critique.

    Yes. I would phrase it something like this: $L = \{[a,b,c]|a=0\}$ To see that $[a,b,c]=[0,0,0]\in L$ just note that $a=0$.
    (I have used rows instead of columns to save typing. The idea is the same.)
    Last edited by Walagaster; Sep 28th 2018 at 10:25 AM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Apr 2005
    Posts
    20,044
    Thanks
    3173

    Re: Proving that a subset of R^3 is a subspace (or not), and proof critique.

    The set of vectors, [a, b, c] with the condition that a= 0 is just the set of all [0, b, c] where b and c can be any numbers. In particular, b and c can be 0 which gives the zero vector, [0, 0, 0].
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof critique
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Feb 3rd 2011, 09:22 PM
  2. [SOLVED] Critique my proof?
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: Aug 23rd 2010, 06:35 AM
  3. Subspace Test Proof (of test not subset)
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Mar 15th 2010, 10:58 AM
  4. subset U subset is NOT subspace of Superset?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Sep 20th 2009, 05:17 PM
  5. Help proving a subset is a subspace
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Apr 16th 2009, 06:31 PM

Search tags for this page

Click on a term to search for related topics.

/mathhelpforum @mathhelpforum