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Get Full Access to Linear Algebra: A Geometric Approach - 2 Edition - Chapter 5.2 - Problem 15
Get Full Access to Linear Algebra: A Geometric Approach - 2 Edition - Chapter 5.2 - Problem 15

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# (from the 1994 Putnam Exam) Let A and B be 2 2 matrices with integer entries such that ISBN: 9781429215213 438

## Solution for problem 15 Chapter 5.2

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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##### ISBN: 9781429215213

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