\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
In \(\mathbb{R}^4\), let \(F = \{(x, y, z, t) \in \mathbb{R}^4 : x + y = 0 \text{ and } z = t\}\). Find a basis of \(F\), then complete it into a basis of \(\mathbb{R}^4\) adapted to \(F\).
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