/*! 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} Q6E det(4A)=4detA聽for all聽4脳4 mat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q6E (page 308)

det(4A)=4detAfor all4脳4 matricesA.

Short Answer

Expert verified

Therefore, the given condition is not satisfied. So, the given statement is false.

Step by step solution

01

Definition. 

A determinant is a unique number associated witha square matrix.

A determinant is a scalar value that is a function of the entries of a square matrix.

It is the signed factor by which areas are scaled by this matrix. If the sign is negative the matrix reverses orientation.

02

To check whether the given condition is true or false.. 

For example, if

A=I

then,

detA=1.

But,

det4A=det4I=16鈮�4detA.

We get,

det(4A)=44det(A)because, all the four columns are multiplied by 4.

Therefore, the given condition is not satisfied. So, the given statement 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 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

In Exercises 62 through 64, consider a function from to that is linear in both columns and alternating on the columns. See Examples 4 and 6 and the subsequent discussions. Assume that .


64. Using Exercises 62 and 63 as a guide, show that D(A)=ad-bc=detAfor all 2脳2matrices A .

Find the determinants of the linear transformations in Exercises 17 through 28.

27. T(f)=af'+bf", where a and b are arbitrary constants, from the space V spanned by cos(x)and sin(x)to V

det[0100001000011000]=1

There exist invertible2脳2matrices A andBsuch thatdet(A+B)=detA+detB .

Ifu鈫�,v鈫�,w鈫�are three unit vectors in鈩�3, what are the possible values ofdet[u鈫�v鈫�w鈫�]?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Mechanics 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.