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We call the vector x Rn integral if every component xi is an integer. Let A be a

Linear Algebra: A Geometric Approach | 2nd Edition | ISBN: 9781429215213 | Authors: Ted Shifrin, Malcolm Adams ISBN: 9781429215213 438

Solution for problem 8 Chapter 5.2

Linear Algebra: A Geometric Approach | 2nd Edition

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Linear Algebra: A Geometric Approach | 2nd Edition | ISBN: 9781429215213 | Authors: Ted Shifrin, Malcolm Adams

Linear Algebra: A Geometric Approach | 2nd Edition

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Problem 8

We call the vector x Rn integral if every component xi is an integer. Let A be a nonsingular n n matrix with integer entries. Prove that the system of equations Ax = b has an integral solution for every integral vector b Rn if and only if det A = 1. (Note that if A has integer entries, A maps integral vectors to integral vectors. When does A map the set of all integral vectors onto the set of all integral vectors?)

Step-by-Step Solution:
Step 1 of 3

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Step 2 of 3

Chapter 5.2, Problem 8 is Solved
Step 3 of 3

Textbook: Linear Algebra: A Geometric Approach
Edition: 2
Author: Ted Shifrin, Malcolm Adams
ISBN: 9781429215213

Linear Algebra: A Geometric Approach was written by and is associated to the ISBN: 9781429215213. The answer to “We call the vector x Rn integral if every component xi is an integer. Let A be a nonsingular n n matrix with integer entries. Prove that the system of equations Ax = b has an integral solution for every integral vector b Rn if and only if det A = 1. (Note that if A has integer entries, A maps integral vectors to integral vectors. When does A map the set of all integral vectors onto the set of all integral vectors?)” is broken down into a number of easy to follow steps, and 83 words. This textbook survival guide was created for the textbook: Linear Algebra: A Geometric Approach, edition: 2. This full solution covers the following key subjects: . This expansive textbook survival guide covers 31 chapters, and 547 solutions. The full step-by-step solution to problem: 8 from chapter: 5.2 was answered by , our top Math solution expert on 03/15/18, 05:30PM. Since the solution to 8 from 5.2 chapter was answered, more than 208 students have viewed the full step-by-step answer.

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We call the vector x Rn integral if every component xi is an integer. Let A be a