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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

    Dick

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    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

    Dick

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    Ok. But you might want to pick a little more substantial practice question.
     
  6. Mar 11, 2014 #5
    Looking forward to doing so.
     
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