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Math Help - linearly dependent scalars

  1. #1
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    linearly dependent scalars

    Let v, w be elements of a vector space and assume v does not equal 0. If v, w are linear dependent, show that there is a number x such that w=xv. Thanks for any help, Mark.
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  2. #2
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    By definition of dependence \alpha v + \beta w = 0\;\& \,\alpha  \ne 0 \vee \beta  \ne 0.
    Then if \beta  = 0 then \alpha v = 0.
    But \alpha  \ne 0\, \Rightarrow \,v = 0 which is a contradiction.
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