Recall that a map has an inverse if and only if the map is 1-1 and onto. Prove that an affine map A : V → W has an inverse if and only if the same is true of its linear part L. [Hint: Express A-1 in terms of L-1.]

Recall that a map has an inverse if and only if the map is 1-1 and onto. Prove that an affine map A : V → W has an inverse if and only if the same is true of its linear part L. [Hint: Express A-1 in terms of L-1.]

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 24EQ

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15. Recall that a map has an inverse if and only if the map is 1-1 and onto.
Prove that an affine map A : V → W has an inverse if and only if the
same is true of its linear part L. [Hint: Express A1 in terms of L-.]

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