Theorem: a set of vectors is linearly independent if and only if whenever a linear combination is 0

Created almost 9 years ago, updated about 8 hours ago

Independence means that whenever $\sum_i c_iv_i=0$, all coefficients vanish. The universal quantifier is important: finding one zero combination with all coefficients zero proves nothing, because every list has that combination. To disprove independence, exhibit a single nontrivial relation.

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