\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Find a generating family of the subspace $$ F = \{(x, y, z, t) \in \mathbb{R}^4 : x + y - z - t = 0 \ \text{ and } \ 3x - y - z + t = 0\} $$ of \(\mathbb{R}^4\).
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