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Question on Remark in Axler's Linear Algebra

  1. Feb 18, 2012 #1
    Hello, i am studying vector subspacess and Axler introduces the two criteria for a vector subspace (closure under addition and scalar multiplication).
    He then proceeds to give an example; (x1,x2,x3,x4) belonging to F^4 : x3=x4+b, where b is an element of F. Axler states that this example is not a subspace unless b=0, yet this is the same space as V and i was under the impression (Axler states it himself) that V is a subspace of itself? Should not any value of b in F be possible?
  2. jcsd
  3. Feb 19, 2012 #2
    I think i have realised where i went wrong. The zero vector must be contained within the subspace, thus b=0 is the only solution which allowes this. Is that a suitable method to complete the example or am i missing something else?
  4. Feb 19, 2012 #3


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    that is correct.
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