Prove Corollary 6.2. If L: V → W is a linear transformation of a vector space V into a vectorspace W and dim V=dim W, then the following statements are true:(a) If L is one-to-one, then it is onto.(b) If L is onto, then it is one-to-one.

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Answered: Prove Corollary 6.2. If L: V → W is a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Prove Corollary 6.2. If L: V → W is a linear transformation of a vector space V into a vector space W and dim V=dim W, then the following statements are true: (a) If L is one-to-one, then it is onto. (b) If L is onto, then it is one-to-one.