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San of a subspace

  1. Sep 13, 2014 #1
    1. The problem statement, all variables and given/known data

    If x is a subspace of V so, span(x)=x

    2. Relevant equations

    span(x)=x


    3. The attempt at a solution

    If x is a subspace so, for any "a", "b" in x:
    a+b∈x
    and (c1)*a∈x

    So a linear combination of x belongs to x but is equal to x?
     
  2. jcsd
  3. Sep 14, 2014 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Your last sentence is badly worded. There is no such thing as "a linear combination of x". You mean "a linear combination of vectors in x".

    What you have proved is only one direction- you have proved that the span of x is a subset of x. Now you need to prove that x is a subset of span of x. That is easy. Suppose a is vector in x. Then 1a is in the span of x.
     
  4. Sep 14, 2014 #3
    Hi, thanks!
     
    Last edited: Sep 14, 2014
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