\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
In \(\mathbb{R}^3\) (generated by the canonical basis of cardinal \(3\)), show that any family of \(4\) or more vectors is dependent. Apply this to conclude that \(\bigl((1, 2, 3), (4, 5, 6), (7, 8, 9), (1, 1, 1)\bigr)\) is dependent without computing.
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