Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 6: Q.6.1-47E (page 276)

If A and B are orthogonal $n 脳 n$ matrices such that $A = d e t B = 1$ , then matrices A and B must commute.

Short Answer

Expert verified

Therefore,

$A 鈮� B$

So, the given statement is false.

Step by step solution

Orthogonal Matrix Definition

A square matrix with real numbers or elements is said to be an orthogonal matrix, if its transpose is equal to its inverse matrix.

Or we can say, when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.

To check whether the given condition is true or false

For example,

$A = [\begin{matrix} 0 & 1 & 0 \\ - 1 & 0 & 0 \\ 0 & - 1 & 0 \end{matrix}] B = [\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & - 1 & 0 \end{matrix}]$

Clearly, bothandare orthogonal matrices, and.

However,

$A B = [\begin{matrix} 0 & 0 & 1 \\ - 1 & 0 & 0 \\ 0 & - 1 & 0 \end{matrix}]$

$A B 鈮� [\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{matrix}] A B 鈮� B A$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

If A and B are orthogonal $n 脳 n$ matrices such that $A = d e t B = 1$ , then matrices A and B must commute.

Short Answer

Step by step solution

Orthogonal Matrix Definition

To check whether the given condition is true or false

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Statistics

Probability and Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

91影视

If A and B are orthogonal n脳nmatrices such that A=detB=1 , then matrices A and B must commute.

Short Answer

Step by step solution

Orthogonal Matrix Definition

To check whether the given condition is true or false

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Statistics

Probability and Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

If A and B are orthogonal $n 脳 n$ matrices such that $A = d e t B = 1$ , then matrices A and B must commute.