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!

Homework Help: Subset and subspace

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

    Show that if V is a subspace of R n, then V must contain the zero vector.

    3. The attempt at a solution

    If a set V of vectors is a subspace of Rn, then, V must contain the zero vector, must be closed under addition, and, closed under scalar multiplication.

    Let u = (u1,u2,u3....un), Let w = (w1,w2,w3...wn) and k scalar is a real number.

    for ku = (0,0,0,.....0n), k = 0 (is this a valid?)

    for u+w = 0, (u1+w1, u2+w2,u3+w3....un+wn) = (0,0,0,.....0n)

    i.e., u1+w1 = 0, then u1=-w1
    if u1 = 1,then w1=-1 (is this valid?)
  2. jcsd
  3. Mar 11, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper

    If your definition of V being a 'subspace' includes that V contains the zero vector, then there's not much to show. Is there?
  4. Mar 11, 2014 #3
    Well, yea. But I thought it was a good way for the practice question to brush up my conceptual understanding of subspace. It's pretty nebulous at the moment.
  5. Mar 11, 2014 #4


    User Avatar
    Science Advisor
    Homework Helper

    Ok. But you might want to pick a little more substantial practice question.
  6. Mar 11, 2014 #5
    Looking forward to doing so.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted