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Math Help - Vector spaces and span

  1. #1
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    Vector spaces and span

    If Z_13 = F and V_F = span ((1,1), (1,2)), how many elements does V_F have?

    I can find nothing in my book or on the internet that explains how to do this. Please help! Thanks in advance!

    I understand that the general form for all vectors in the vector space is (a+b, a+2b) for this particular span. This means that the components of the vector can't be the same, so would it be 156 instead? You wouldn't be able to have (0,0), (1,1), (2,2), etc. Is this correct?
    Last edited by scosgurl; February 15th 2009 at 06:37 PM. Reason: adding information/double-checking understanding
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  2. #2
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    Quote Originally Posted by scosgurl View Post
    If Z_13 = F and V_F = span ((1,1), (1,2)), how many elements does V_F have?

    I can find nothing in my book or on the internet that explains how to do this. Please help! Thanks in advance!
    13*13= 169. (1,1) and (1,2) are independent so x(1,1)+ y(1,2) are distinct vectors for all x and y in Z_13.
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