/*! 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} Q11E For each of the matrices in Exer... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q11E (page 336)

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.

[51-521082-7]

Short Answer

Expert verified

Eigenvalues are:

位=-1,almu-1=1

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

Since, given matrix is triangular its eigenvalues arethe entries on the main diagonal, which are 1 and 2. Since, each one of them appear twice in said diagonal, both eigenvalues鈥� algebraic multiplicities are 2.

detA-位滨=05-位1-521-位082-7-位=05-位1-位-7-位-20+401-位-2-7-位=0-位2-1位+1=0位1=i,位2=-i,位3=-1

Hence, the answer is:

位3=-1,almu-1=1

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

Is v鈬赌an eigenvector ofA+2In? If so, what is the eigenvalue?

Consider the matrixA=|1k11|where k is an arbitrary constant. For which values of k does A have two distinct real eigenvalues? When is there no real eigenvalue?

23: Suppose matrix A is similar to B. What is the relationship between the characteristic polynomials of A and B? What does your answer tell you about the eigenvalues of A and B?

Is v鈬赌an eigenvector ofA3 ? If so, what is the eigenvalue?

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.

Rotation through an angle of 180掳inR2.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

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.