Question: Let H be a hyperplane in a linear space X. Then H is parallel to unique subspace V such that 1. x0 V

Let H be a hyperplane in a linear space X. Then H is parallel to unique subspace V such that 1. x0 ∈ V ⇔ H = V
2. V ⊂ X
3. X = lin{V, x1} for every x1 ∉ V
4. for every x ∈ X and x1 ∉ V, there exists a unique α ∈ R such that x = ax1 + v for some v ∈ V

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