\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Extract a basis of \(\mathbb{R}^3\) from the generating family \(\bigl((1, 0, 0), (0, 1, 0), (1, 1, 0), (0, 0, 1), (1, 0, 1)\bigr)\).
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