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Prove that if two vectors are linearly dependent, one of them is a scalar multiple of the other?

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If $v,w$ are linearly dependent so there is constants $c_1,c_2$ which both are not zero at the same time and $c_1v+c_2w=0$. Let $c_1\neq 0$ so by dividing, we have $v=\frac{-c_2}{c_1}w$.

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