Unformatted text preview: M ◦ L is onetoone. (b) Give an example where M is not onetoone, but M ◦ L is onetoone. (c) Is it possible to give an example where L is not onetoone, but M ◦ L is onetoone? Explain. 5. 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) Deﬁne 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 09/30/2011 for the course MATH 235 taught by Professor Celmin during the Spring '08 term at Waterloo.
 Spring '08
 CELMIN
 Vector Space

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