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(from the 1994 Putnam Exam) Let A and B be 2 2 matrices with integer entries such that

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

Solution for problem 15 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 15

(from the 1994 Putnam Exam) Let A and B be 2 2 matrices with integer entries such that A, A + B, A + 2B, A + 3B, and A + 4B are all invertible matrices whose inverses have integer entries. Prove that A + 5B is invertible and that its inverse has integer entries. (Hint: Use Exercise 7.)

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7.4 Exponential and Logarithmic Equations Copyright © Cengage Learning. All rights reserved. Introduction There are two basic strategies for solving exponential or logarithmic equations. The first is based on the One-to-One Properties and the second is based on the Inverse Properties. One-to-One Properties a = a if and only if x = y. logax = log a if and only if x = y. Inverse Properties a loa = x log a = x 2 Solving Simple Equations 3 Introduction 4 Example 1 Solve for x. a) 64 3x ▯ 32 2

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Chapter 5.2, Problem 15 is Solved
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Textbook: Linear Algebra: A Geometric Approach
Edition: 2
Author: Ted Shifrin, Malcolm Adams
ISBN: 9781429215213

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(from the 1994 Putnam Exam) Let A and B be 2 2 matrices with integer entries such that