/*! 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} Q36E 36.聽Suppose A is an聽n脳n matri... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q36E (page 309)

36.Suppose A is ann脳n matrix and Bis obtained fromAby swapping two rows of A. IfdetB<detA, then A must be invertible.

Short Answer

Expert verified

Therefore,detA<detB . So, the given statement is true.

Step by step solution

01

Matrix Definition

Matrix is a set of numbers arranged in rowsand columns so as to form a rectangular array.

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

If A were a non-invertible matrix, and B were obtained from A by switching two rows,

then

detB=0=detA,

Which means detB鈮�detA.

So, if detB鈮�detA, then A is invertible. So, the given statement 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

The determinant of any diagonaln脳nmatrix is the product of its diagonal entries.

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

In an economics text,10we find the following system:

sY+ar=I掳+GmY-hr=Ms-M

Solve for Y and r.

The equation det(-A)=detAholds for all 6脳6matrices.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

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.