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Let \(\lambda \in \mathbb{R}\). Find a necessary and sufficient condition on \(\lambda\) for \(F = \mathrm{Vect}\bigl((\lambda, \lambda, 1)\bigr)\) and \(G = \mathrm{Vect}\bigl((1, \lambda, 1), (2, 1, 1)\bigr)\) to be in direct sum in \(\mathbb{R}^3\).
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