This may be a really simple proof but its giving me grief.(adsbygoogle = window.adsbygoogle || []).push({});

If {[itex]v_1, v_2, v_3[/itex]} is a linearly dependent set of vectors in [itex]\mathbb{R}^n[/itex], show that {[itex]v_1, v_2, v_3, v_4[/itex]} is also linearly dependent, where [itex]v_4[/itex] is any other vector in [itex]\mathbb{R}^n[/itex].

Any hints on where to start? I started out by writing out all the claims that could be made by taking the first set of vectors to be linearly independent, but that didn't get me terribly far.

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# Proof of linear dependence

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