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Let H1 and H2 be subspaces of R^n. Prove that the intersection of H1 and H2...

Let H1 and H2 be subspaces of R^n. Prove that the intersection of H1 and H2 is a subspace of R^n. Will the union of H1 and H2 always be a subspace of R^n? I'm pretty lost here so please show/explain every step! Thanks!

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