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Span and dimension

  1. Sep 14, 2014 #1
    1. The problem statement, all variables and given/known data

    Hi, I have to prove that there's no exist a generating set for "x" with less of "n" vectors when "n" is the dimension of the basis of "x"

    2. Relevant equations
    is there a span(x) whith dimension m? when m<n and n is the dimension of the basis

    3. The attempt at a solution

    I know that all the basis of a vectorial space must have the same dimension, and the basis have linearly independient vectors, so I cant remove any of them, but I dont know how sow that its not possible that existence of that span
     
  2. jcsd
  3. Sep 16, 2014 #2

    BruceW

    User Avatar
    Homework Helper

    to start this proof, I think you need to start with a mathematical definition of what a basis actually is.
     
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