1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Subset and subspace

  1. Mar 11, 2014 #1
    1. The problem statement, all variables and given/known data


    a) Find a set of vectors in R2 that is closed under vector addition but not under scalar multiplication
    Find a set of vectors closed under scalar multiplication but not closed under vector addition.

    3. The attempt at a solution

    a) Let S be a set of vectors in R2.

    S = {(x,y) | x + y =0}
    x = (1,1) y = (-1,-1)

    To show that S set of vectors is closed under vector addition, x + y must remain in S.

    x + y = (x1 + y1, x2+y2) = ( 0,0)

    Am I right up till here?
     
  2. jcsd
  3. Mar 11, 2014 #2

    Mark44

    Staff: Mentor

    No. Your set S is the line whose equation is x + y = 0. This is a line through the origin, and as such, this set is a one dimensional subspace of R2. You need to find a different set of vectors.

    Look at the examples in your book or notes. There are probably some examples of sets that are closed under one operation, but not the other.

    Also note that this is two problems - one for a set that is closed under vector addition but not under multiplication by a scalar; the other is closed under scalar multiplication but not vector addition.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Subset and subspace
  1. Subsets and subspace (Replies: 2)

  2. Subset and subspace (Replies: 15)

  3. Subspace and subset (Replies: 10)

  4. Subset and subspace (Replies: 4)

Loading...