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Unformatted text preview: V . Prove that the following are equivalent. 1) L1 exists. 2) L is onetoone. 3) Null( L ) = { ~ } 4) L is onto. 4. Let V and W be vector spaces with dim V = n and dim W = m , let L : V W be a linear mapping, and let A be the matrix of L with respect to bases B for V and C for W . a) Dene an explicit isomorphism from Range( L ) to Col( A ). Prove that your map is an isomorphism. b) Use a) to prove that rank( L ) = rank( A )....
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This note was uploaded on 11/30/2010 for the course MATH 235/237 taught by Professor Wilkie during the Spring '10 term at Waterloo.
 Spring '10
 WILKIE
 Vector Space

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