Let u and v be vectors in a vector space V. (a) Let H be any...

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Let u and v be vectors in a vector space V. (a) Let H be any subspace of V that contains both u and v. Explain briefly why H also contains Span {u, v}. (b) Suppose {u, v} forms a basis for a subspace W of V. Then show that {u, v + u} is also a basis for W. Let u and v be vectors in a vector space V. (a) Let H be any subspace of V that contains both u and v. Explain briefly why H also contains Span {u, v}. (b) Suppose {u, v} forms a basis for a subspace W of V. Then show that {u, v + u} is also a basis for W.