/*! 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} Q7E 7:聽For each of the matrices in ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q7E (page 336)

7:For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.

l3

Short Answer

Expert verified

Eigenvalues is: 位=1, almu(1)=3.

Step by step solution

01

Eigenvalues

  • In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by 位, is the factor by which the eigenvector is scaled.
  • Eigenvalues of a triangular matrix are its diagonal matrix.
02

Step 2: Finding all real eigenvalues, with their algebraic multiplicities

We can clearly see that,

The matrix I3 is diagonal, so its eigenvalues are the entries on the main diagonal, which is only 1. Since it appears three times on said diagonal, its multiplicity is 3.

Hence, the answer is 位=1, almu(1)=3.

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

Arguing geometrically, find all eigenvectors and eigenvalues of the linear transformations in Exercises 15 through 22. In each case, find an eigenbasis if you can, and thus determine whether the given transformation is diagonalizable.

Orthogonal projection onto a line L in R3.

25: Consider a positive transition matrix

A=[abcd]

meaning that a, b, c, and dare positive numbers such that a+ c= b+ d= 1. (The matrix in Exercise 24 has this form.) Verify that

[bc]and[1-1]

are eigenvectors of A. What are the associated eigenvalues? Is the absolute value of these eigenvalues more or less than 1?

Sketch a phase portrait.

Is v鈬赌an eigenvector of 7 A? If so, what is the eigenvalue?

If a 2 脳 2 matrix A has two distinct eigenvalues位1and位2, show that A is diagonalizable.

For a given eigenvalue, find a basis of the associated eigenspace. Use the geometric multiplicities of the eigenvalues to determine whether a matrix is diagonalizable. For each of the matrices A in Exercises 1 through 20, find all (real) eigenvalues. Then find a basis of each eigenspace, and diagonalize A, if you can. Do not use technology

0-112
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Decision 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.