# Test2 - Math 332 Test 2 Printed Name Please carefully work...

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Math 332 – Test 2 Printed Name: Please carefully work all of the following problem(s). You must SHOW YOUR WORK to receive ANY credit! 1 Please answer the following questions. A 7 pts [1] Let V be a vector space. Suppose W V . Carefully deﬁne what it means when we say W is a subspace of V . B 7 pts [1] Let f : V W be a mapping between any two vector spaces and suppose U W . Deﬁne, using set builder notation, f - 1 [ U ]. C 7 pts [1] Let V be a vector space and suppose B ⊂ V . Deﬁne what is meant when we say B is a basis. D 7 pts [1] State the Rank-Nullity Theorem. E 7 pts [1] Let f : V W be a mapping between any two vector spaces. Deﬁne what it means when we say f is an isomorphism. Dr. Emmert Spring 2010 I of IV Points Earned of 35

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Math 332 – Test 2 2 15 pts [4] Please carefully answer one of the following two statements A Grade Me Let V be a vector space. Let S = { u 1 , u 2 ,..., u k } be any nonempty subset of V . Show that Span( S ) is a subspace of V . B
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Test2 - Math 332 Test 2 Printed Name Please carefully work...

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