1. This question is about subspaces and bases. Let H₁R be the hyperplane defined in normal form by and H₂ CR¹ the hyperplane defined in normal form by 0. Let A = H₁nH₂≤R and B = H₁U H₂ ≤R4. Determine whether each of the subsets A and B are subspaces or not. If they are subspaces, prove it using the definition and find a basis; if not, explain why.

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