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Prove that every permutation matrix is orthogonal

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

Solution for problem 5.1.25 Chapter 5

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 5.1.25

Prove that every permutation matrix is orthogonal.

Step-by-Step Solution:
Step 1 of 3

Math121 Chapter 3 Lesson 3.4 – Parallel and Perpendicular Lines EXAMPLE 1. 4x + 2y = 10 (First, we’re asked to put this in y = mx + b form.) 2y = -4x + 10 y = -2x + 5 (Now, we’re asked to find the equation for a line that is parallel to the line made by the linear equation we just got… and it runs through the point (8, 2). So, take the x and y from the point we were given, and…substitute it in to the linear equation we wrote. Remember, a parallel line means that it will have the exact same slope as the original line.) 2 = -2 (8) + b (Now, solve for b.) b = 18 (Now that we have b, we can substitute this into a new equation for the line parallel to the one in the original equation, using the same slope.) y = -2x + 18 (This is the linear equation to the line parallel to the original!) EXAMPLE 2. 2(y – 1) + ((4x + 5)/3) = -4 (First, we’re asked to put this in slope- intercept form, which is y = mx + b form. But we need to get y on a side by itself first, so…to get rid of the fraction,

Step 2 of 3

Chapter 5, Problem 5.1.25 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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Prove that every permutation matrix is orthogonal