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Homework Help: Dimension Proof?

  1. Feb 17, 2009 #1
    1. The problem statement, all variables and given/known data
    Let U, W be subspaces of a vector space V. Show that dim(U+W) = dim(U) + dim (W) - dim (U intersect W).

    2. Relevant equations

    3. The attempt at a solution
    I can see this picture-wise in a venn-diagram form. In adding U and W you count the elements in their intersection twice, since both spaces contain them. Thus, you subtract the dimension of U intersect W. But, how do you show this in proof format? It doesn't seem like a verbal explanation is enough.
  2. jcsd
  3. Feb 17, 2009 #2


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    Homework Helper

    What you really are thinking about in your Venn diagram are basis vectors. Write a basis for U intersect W. Extend it to a basis for U and W. Now do the Venn argument.
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