# linearly dependent scalars

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• February 15th 2009, 06:53 AM
mark talarico
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.
• February 15th 2009, 09:59 AM
Plato
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.