\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that \(\mathcal{F} = \bigl((1, 1, 1), (1, 1, 0), (1, 0, 0)\bigr)\) is a basis of \(\mathbb{R}^3\) using the basis characterisation in dimension \(n\).
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