/*! 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} Q50E .聽Find the determinant of the m... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q50E (page 292)

.Find the determinant of the matrixMn=[111...1122...2123...3鈰�鈰�鈰�鈰�鈰�123...n]for arbitrary n. (Theij thentry of Mnis the minimum of i andj).

Short Answer

Expert verified

Therefore, the determinant of the given matrix is given by,

detMn=1,鈭赌n鈭�鈩�

Step by step solution

01

Definition

A determinant is a unique number associated with asquare 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

Given

Given matrix,

Mn=111鈰�1122鈰�2123鈰�3鈰�鈰�鈰�鈰�鈰�123鈰�n

03

To find determinant

If we multiply the(n鈭�1)-th row and add it to then-th row, then-th row will become

0鈥�01 , but the determinant will stay the same.


Now, using Laplace expansion along the n -th row, we can see that. Since, we conclude that

detMn=detMn鈭�1

SincedetM1=1we conclude thatdetMn=1,鈭赌n鈭�鈩�

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

det(A+B)=detA+detBfor all5脳5 matricesA andB.

Question:We say that a linear transformation Tfrom N3toN3to preserves orientation if it transforms any positively oriented basis into another positively oriented basis. See Exercise 19. Explain why a linear transformationT(x鈫�)=Ax鈫�preserves orientation if (and only if) detAis positive.

Consider a 4x4 matrix A with rows V1鈫�,V2鈫�,V3鈫�,V4鈫�. If det(A) = 8, find the determinants in Exercises 11 through 16.

16. role="math" localid="1659506283449" det[6v鈬赌1+2v鈬赌4v鈬赌2v鈬赌33v鈬赌1+v鈬赌4]

What is the area of the largest ellipse you can inscribe into a triangle with side lengths 3,4 , and 5 ? Hint: The largest ellipse you can inscribe into an equilateral triangle is a circle.

IfA is an n脳n matrix of rank n-1, what is the rank of adj(A)? See Exercises 42 and 43.

See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

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.