Unformatted text preview: M ◦ L is one-to-one. (b) Give an example where M is not one-to-one, but M ◦ L is one-to-one. (c) Is it possible to give an example where L is not one-to-one, but M ◦ L is one-to-one? 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 )....
View Full Document
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
- Vector Space