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Let (a) Show that (b) Prove, by mathematical induction, that An for n 1c 0 1 1 1 d . A 1

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition | ISBN: 9780538735452 | Authors: David Poole ISBN: 9780538735452 298

Solution for problem 3.1.38 Chapter 3

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition | ISBN: 9780538735452 | Authors: David Poole

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Problem 3.1.38

Let (a) Show that (b) Prove, by mathematical induction, that An for n 1c 0 1 1 1 d . A 1

Step-by-Step Solution:
Step 1 of 3

InEqualities: 9/2/16 -Less than: Less than or equal to Greater than Greater than or equal to AB A≥B Transitivity: -If A0 - D-B>0 - Therefore (D+C) – (A+B) >0 - Therefore D+C > A+B Mult. Of Inequalities: - If A>B… If C>0 AC>BC  -3>-6 A=1, B=2, C= -3 Mult. Inverse: - Given a number ,X, the inverse is what the mult. X to get a product of 1. - -2/3 -> -3/2 - Find all numbers X, such that… X-8/X-4 < 3 X-4/1 × X-8/X-4 < 3(X-4) X-8 < 3(X-4) Case 1: X-4 > 0 Case 2: X-4 < 0 X > 4 X < 4 X-8 < 3(X-4) X-8 > 3(X-4) X-8 < 3X-12 X-8 > 3X-12 -8 < 2X-12 -8 > 2X-12 4 < 2X 4 > 2X 2 < X 2 > X Solution: X > 4 & X < 2 Additive inverse of Inequalities: - If A -B

Step 2 of 3

Chapter 3, Problem 3.1.38 is Solved
Step 3 of 3

Textbook: Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign)
Edition: 3
Author: David Poole
ISBN: 9780538735452

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Let (a) Show that (b) Prove, by mathematical induction, that An for n 1c 0 1 1 1 d . A 1