/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none}

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q7E (page 233)

If then脳nmatrices Aand Bare orthogonal, which of the matrices in Exercise 5 through 11 must be orthogonal as well?AB.

Short Answer

Expert verified

The Matrix AB is orthogonal.

Step by step solution

01

Definition of Orthogonal transformation

Ann脳n matrix Ais orthogonal if and only if its columns form an orthonormal basis of鈩�n.

02

Verification whether the given matrix is orthogonal.

Given thatA andB are orthogonal matrices.

By theorem: The Product AB of two orthogonaln脳n matricesA andB is orthogonal.

Therefore,AB is an orthogonal matrix.

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

Most popular questions from this chapter

TRUE OR FALSE?If matrix A is orthogonal, then the matrixAT must be orthogonal as well.

If A and B are arbitraryn脳n matrices, which of the matrices in Exercise 21 through 26 must be symmetric?

B(A+A螕)B螕.

Show that an orthogonal transformation LfromRn to Rnpreserves angles: The angle between two nonzero vectorsv鈯� andw鈯�inRnequals the angle betweenL(v鈯�) andL(w鈯�) .Conversely, is any linear transformation that preserves angles orthogonal.

If then脳n matrices Aand Bare orthogonal, which of the matrices in Exercise 5 through 11 must be orthogonal as well?B-1.

If the nxnmatrices Aand Bare orthogonal, which of the matrices in Exercise 5 through 11 must be orthogonal as well? B-1AB.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.