/*! 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} Q10E There exists a real 5 脳 5 matri... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q10E (page 383)

There exists a real 5 脳 5 matrix without any real eigenvalues.

Short Answer

Expert verified

False, that without any real eigenvalues there exists a real 5 脳 5 matrix.

Step by step solution

01

Define eigenvalue:

Eigenvalues is a special set of scale values associated with a set of line numbers in almost matrix measurements.

02

Explanation for the real 5 × 5 matrix without any real eigenvalues:

If a complex number Z is an eigenvalue of a matrix , then it is a root of det (A-位濒)which is a polynomial, so its complex conjugate zmust also be an eigenvalue of . Thus, since a 5脳5 matrix has 5 eigenvalues (counting their algebraic multiplicities), then at least one of them must be a real one

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

Show that 4 is an eigenvalue ofA=[-66-1513],and find all corresponding eigenvectors.

Two interacting populations of coyotes and roadrunners can be modeled by the recursive equations

h(t + 1) = 4h(t)-2f(t)

f(t + 1) = h(t) + f(t).

For each of the initial populations given in parts (a) through (c), find closed formulas for h(t) and f(t).

(a)h(0)=f(0)=100(b)h(0)200,f(0)=100(c)h(0)600,f(0)=500

Question: If a vectorv鈫�is an eigenvector of both AandB, isv鈫� necessarily an eigenvector ofAB?

TRUE OR FALSE

18. If A and B are nxn matrices, if 伪is an eigenvalue of A, and if 尾is an eigenvalue of B, then 伪尾 must be an eigenvalue of AB.

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

15.(-101-301403)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

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.