\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(F = \mathrm{Vect}(1, X, X^2)\) and \(G = \mathrm{Vect}(X^2, X^3)\) in \(\mathbb{R}_3[X]\). Compute \(\dim F\), \(\dim G\), \(\dim(F + G)\), \(\dim(F \cap G)\).
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