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In \(\mathcal{M}_2(\mathbb{R})\), recall \(\mathcal{S}_2(\mathbb{R}) \oplus \mathcal{A}_2(\mathbb{R}) = \mathcal{M}_2(\mathbb{R})\) (symmetric and skew-symmetric decomposition). Write a basis of \(\mathcal{M}_2(\mathbb{R})\) adapted to this decomposition.
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