1. Limited time only! Sign up for a free 30min personal 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!

Subspace question

  1. Mar 18, 2013 #1
    1. The problem statement, all variables and given/known data

    Determine whether the following is a Subspace of r^3:

    All vectors of the form (a,b,c), where b=a+c

    3. The attempt at a solution

    The answer in the book says it is not a subspace but I can only find examples that show it is a Subspace I.e.

    Let u=(a,a+c,c)=(1,2,1), v=(a,a+c,c)=(2,4,2) and k=2 then

    U+v=(3,6,3)=(a,a+c,c) so it's closed under addition

    Ku=2(a,a+c,c)=2(1,2,1)=(2,4,2)=(a,a+c,c) so it is closed under scalar multiplication

    Maybe I don't understand the concept correctly am I doing something wrong?
  2. jcsd
  3. Mar 18, 2013 #2


    User Avatar
    Science Advisor

    If your textbook says this is not a subspace, it is wrong. It is, exactly as you say, the subspace of R3 of all vectors of the form (a, b, c)= (a, a+ c, c)= (a, a, 0)+ (0, c, c)= a(1, 1, 0)+ c(0, 1, 1). In other words, it is the two dimensional subspace with (1, 1, 0) and (0, 1, 1) as basis.
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: Subspace question
  1. Subspace Questions (Replies: 6)

  2. Subspaces question (Replies: 1)

  3. Subspace Question (Replies: 5)

  4. Subspace question (Replies: 11)

  5. Subspace Question (Replies: 9)