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Could someone please explain why, if two vectors in a set of three are parallel to each other, that this implies that the whole set of three vectors is linearly dependent? I have tried to show this algebraically and to understand it graphically but I simply cannot see how one implies the other.

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    $\begingroup$ Consider the (mathematical) condition for two vectors to be parallel. Then compare it to the condition that they are dependent. You'll see ... $\endgroup$ – Matti P. Apr 17 at 8:07
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The vectors would be, say, $\mathbf v$, $k\mathbf v$ and $\mathbf w$. Then $$k\mathbf{v}+(-1)k\mathbf{v}+0\cdot\mathbf{w}=\mathbf{0}$$

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  • $\begingroup$ Thanks very much $\endgroup$ – user193203821309 Apr 17 at 8:11

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