/*! 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 6: Q19E (page 309)

If Ais any n x n matrix, thendet(AAT)=det(ATA).

Short Answer

Expert verified

Therefore, the given condition is true.

Step by step solution

01

Matrix Definition. 

Matrix is a set of numbers arranged in rows and columns so as to form a rectangulararray.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an 鈥渕 by n鈥� matrix, written 鈥�m脳n.鈥�

02

To check whether the given condition is true or false. 

It applies,

detAAT=detAdetAT=detAdetA鈭�detA=detAT=detATdetA鈬�detAAT=detATA

Therefore, the given condition is true .

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

IfA is a 4脳4 matrix whose entries are all 1 or -1 , then detAmust be divisible by 8 (i.e., detA=8kfor some integer k).

25. If the determinant of a square matrix is -1, then Amust be an orthogonal matrix.

Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.

2.[123168-2-40]

Is the determinant of the matrix

A=[1100023456710008100098765432100012100034]

positive or negative? How can you tell? Do not use technology.

There exist real invertible 3脳3 matrices A andSsuch that STAS=-A

See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Pure 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.