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Math Help - smallest subspace of V

  1. #1
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    smallest subspace of V

    Show that span(v1,.., vn) is the smallest subspace of V that contains all the vectors in the list (v1,.., vn)...
    i proved that the span is subspace, i need help on the smallest
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  2. #2
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    Quote Originally Posted by mancillaj3 View Post
    Show that span(v1,.., vn) is the smallest subspace of V that contains all the vectors in the list (v1,.., vn)...
    i proved that the span is subspace, i need help on the smallest
    Let L = span(v1,.., vn)
    Let W be a subspace of V smaller than L. i.e. there is a vector 'x' in L [i.e. x is a linear combination of
    (v1,.., vn)] which is not in W
    This leads to a contradiction under two facts about W:
    1. W is a sub-space
    2. W contains
    (v1,.., vn)

    Under this contradiction - we can say any subspace with (v1,v2,,,vn) will have L as a subspace.



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