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Math Help - Characterization of linear dependence.

  1. #1
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    Characterization of linear dependence.

    With S = {v1, .... , vn} (belongs to K^m) are defined the columns of the Matrix A (belongs to K^mxn), prove that:
    S is linear independent exactly then, when r = n.
    S produces K^m exactly then, when r = m.
    S is a Base from K^m exactly then, when r = m = n
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  2. #2
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    Is r the rank of A?
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  3. #3
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    Yes
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