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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.3: Change Of Basis

Problem 21EQ

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Let A = Z. Let R be defined on A x A where x Ry if 4|(x y).
Prove that R is transitive.

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If x and y are elements of an ordered integral domain D, prove the following inequalities. a. x22xy+y20 b. x2+y2xy c. x2+y2xy
28. Let where and are nonempty. Prove that has the property that for every subset of if and only if is onto. (Compare with Exercise 15c.) Exercise 15c. c. For this same and show that.
If e is the unity in an integral domain D, prove that (e)a=a for all aD. [Type here][Type here]
Let f:AA, where A is nonempty. Prove that f a has right inverse if and only if f(f1(T))=T for every subset T of A.
6. For the given subsets and of Z, let and determine whether is onto and whether it is one-to-one. Justify all negative answers. a. b.
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