Unformatted text preview: . 3. Let L be a linear operator on an n dimensional vector space V . Prove that the following are equivalent. 1) L1 exists. 2) L is onetoone. 3) null( L ) = { ~ } 4) L is onto. 4. Let V be an n dimensional vector space with basis B and let S be the vector space of all linear operators L : V → V . Deﬁne T : S → M ( n,n ) by T ( L ) = [ L ] B . a) Prove that T is an isomorphism. b) Use a) to ﬁnd a basis for S ....
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 Spring '10
 WILKIE
 Linear Algebra, Vector Space, Linear map, Isomorphism

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