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Subspaces

The real plane contains the following subspaces exactly:

Dimension	Copies	Subspace
0	\(1 \times\)	the zero subspace, trivially
1	\(\infty\)-many	\(\mathbb{R}^1\) lines through the origin
2	\(1 \times\)	\(\mathbb{R}^2\) itself, trivially