/*! 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} Q25E 25. If the determinant of a squa... [FREE SOLUTION] | 魅影直播

魅影直播

Log out

Learning Materials

Features

Discover

Chapter 6: Q25E (page 309)

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

Short Answer

Expert verified

The given statement is false.

Step by step solution

01

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.

02

To check whether the given condition is true or false

If the determinant of a square matrix is -1, thenmust be an orthogonal matrix or not.

For example,

A=12002

detA=2-12-0

detA=-1

A is not an orthogonal matrix, yet det A = - 1.

Therefore, the given condition is false.

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 魅影直播!

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

Find the area of the triangle defined by [37]and[82].

Which of the following functions F of A=[abcd] are linear in both columns? Which are linear in both rows? Which are alternating on the columns?
role="math" localid="1659502796300" a.F(A)=bcb.F(A)=cdc.F(A)=acd.F(A)=bc-ade.F(A)=c

Consider a linear transformation T(x鈫�)=Ax鈫� from 鈩�2to鈩�2 . Suppose for two vectors v鈫�1 and v鈫�2in 鈩�2 we have T(v鈫�1)=3v鈫�1androle="math" localid="1660719222222" T(v鈫�2)=4v鈫�2 . What can you say about det A ? Justify your answer carefully.

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).

Consider those 4脳4matrices whose entries are all 1 , -1 , or 0 . What is the maximal value of the determinant of a matrix of this type? Give an example of a matrix whose determinant has this maximal value.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Geometry

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.