\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Exhibit a free family of \(2\) vectors in \(\mathbb{R}^3\) that is not a basis of \(\mathbb{R}^3\). What does this say about the exact-cardinal hypothesis of the basis characterisation in dimension \(n\)?
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