\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
In \(\mathbb{R}^4\), let $$F = \mathrm{Vect}\bigl((1, 1, 0, 0),\ (0, 1, 1, 0),\ (0, 0, 1, 1),\ (1, 2, 2, 1)\bigr).$$ Extract a basis of \(F\) and compute \(\dim F\).
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