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Math Help - Linear Independence of A union of sets

  1. #1
    mrtom18
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    Linear Independence of A union of sets

    Hi everyone, would greatly appreciate some help

    Suppose that V is a vector space and U and W subspaces. Assume v= u (direct sum) w

    S and T are basis for U and V respectively.

    s = u1, u2,..., uk and t = w1, w2,...wt

    Show that S U T is a basis for V (U= union)

    I know I have to prove span and linear independence, and have done span, but it is linear independence that Im struggling with. I have tried writing out a relation containing all the elements of SUT with coefficients, and making this equal zero, but I cant see how this shows that the coefficients themselves must also equal zero...

    Thanks in advance, tom.
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  2. #2
    Super Member Rebesques's Avatar
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    Remember that U and W only intersect at 0.
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