Let V be a vector space with subspaces U and W. Define the sum of U and W to be U W {u w

Chapter 6, Problem 6.1.48

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Let V be a vector space with subspaces U and W. Define the sum of U and W to be U W {u w : u is in U, w is in W} (a) If V 3 , U is the x-axis, and W is the y-axis, what is U W? (b) If U and W are subspaces of a vector space V, prove that U W is a subspace of V.

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