quiz1-solns - MATH 110 - SOLUTION TO QUIZ 1 LECTURE 1,...

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MATH 110 - SOLUTION TO QUIZ 1 LECTURE 1, SUMMER 2009 GSI: SANTIAGO CA ˜ NEZ Let V be a vector space over a field F , and let U and W be subspaces of V . Prove that U W is a subspace of V . Proof. First, since U and W are both subspaces of V , we know that 0 U and 0 W . Hence 0 U W . Now, let x,y U W . Then x,y U and x,y W . Since U is closed under addition, we have that x + y U , and similarly since W is closed under addition, x + y W . Thus x + y U W so U W is closed under addition.
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This note was uploaded on 08/31/2009 for the course MATH 110 taught by Professor Gurevitch during the Summer '08 term at University of California, Berkeley.

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