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Math Help - Dimension problem (linear algebra)

  1. #1
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    Dimension problem (linear algebra)

    I did out the following problem below, but I'm not sure if it's correct so any help would be appreciated!

    F_3 is the finite field with three elements, where the three elements are {0, 1, 2}. (Addition in F_3 is defined modulo 3, which is another way of saying that 3=0)

    V = (F_3)^5 is a vector space.

    Let S = Span({(1, 1, 1, 2, 1), (1, 1, 2, 1, 1), (1, 2, 1, 1, 1), (2, 1, 1, 1, 1), (1, 1, 1, 1, 2)} ⊂ V. What is the dimension of S? (Remember that 3=0)

    I tried this and here's what I came up with:
    I put the vectors inside the span into a matrix like so:

    1 1 1 2 1
    1 1 2 1 1
    1 2 1 1 1
    2 1 1 1 1
    1 1 1 1 2

    Then I row reduced it to get

    1 0 0 0 0
    0 1 0 0 0
    0 0 1 0 0
    0 0 0 1 0
    0 0 0 0 1


    The rank is 5, so does this mean that the dimension of S is also 5?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by faure72 View Post


    The rank is 5, so does this mean that the dimension of S is also 5?
    yes
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