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Math Help - vector space over finite field

  1. #1
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    vector space over finite field

    This question was confusing me so any explanations would be greatly appreciated!

    The following question deals with F_3, the finite field with three elements (the three elements are 0, 1, 2). (Addition in F_3 is defined modulo 3, which means that 3=0.)

    V = (F_3)^5

    T = {x ε V | x1 + x2 + x3 + x4 + x5 = 0}

    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.

    Does S = T? If so, prove it. If not, show this by exhibiting an element of S which is not an element of T.
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  2. #2
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    Quote Originally Posted by buckaroobill View Post
    This question was confusing me so any explanations would be greatly appreciated!

    The following question deals with F_3, the finite field with three elements (the three elements are 0, 1, 2). (Addition in F_3 is defined modulo 3, which means that 3=0.)

    V = (F_3)^5

    T = {x ε V | x1 + x2 + x3 + x4 + x5 = 0}

    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.

    Does S = T? If so, prove it. If not, show this by exhibiting an element of S which is not an element of T.
    What about [2 2 2 2 2]?
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