Let U and V be subspaces of .a) Show that the union, U V,
Chapter 3, Problem 33E(choose chapter or problem)
Let U and V be subspaces of .a) Show that the union, U ? V, satisfies properties (s1) and (s3) of Theorem 2.b) If neither U nor V is a subset of the other, show that U ? V does not satisfy condition (s2) of Theorem 2. [Hint: Choose vectors u and v such that u is in U but not in V and v is in V but not in U. Assume that u + v is in either U or V and reach a contradiction.](Reference Theorem 1)
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