\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Is \(\{M \in M_2(\mathbb{R}) : \mathrm{tr}(M) = 1\}\) a subspace of \(M_2(\mathbb{R})\)? And is \(\{(x, y, z) \in \mathbb{R}^3 : x + y + z = 1\}\) a subspace of \(\mathbb{R}^3\)? Justify briefly the difference between linear and affine equations.
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