/*! 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} Q45E Find all the eigenvalues and 鈥�... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q45E (page 358)

Find all the eigenvalues and 鈥渆igenvectors鈥� of the linear transformations.

T(x0,x1,x2,...)=(0,x0,x1,x2,...)from the space V of infinite sequences into V. (We insert a zero at the beginning.)

Short Answer

Expert verified

The eigenvalue and eigenvector for the given linear transformation is,位=0,E0=0

Step by step solution

01

Define eigenvalues

The scalar values that are associated with the vectors of the linear equations in the matrix are called eigenvalues.

Ax鈫�=位x鈫�,here x鈫�is eigenvector and位 is the eigenvalue.

02

Obtain the eigenvalues and eigenvectors from the given equation

Consider the given equation,

T(x0,x1,x2,...)=(0,x0,x1,x2,...)

Solve,

T(x0,x1,x2,...)=(0,x0,x1,x2,...)(0,x0,x1,x2,...)=位(x0,x1,x2,...)xn=位虫n+1,n鈭�N0,位虫0=0

Hence, this is only possible for位=0 ,in this case, we have

(0,x0,x1,x2,...)=0.(x0,x1,x2,...)=0,0,0,...(x0,x1,x2,...)=00,0,0...

Thus,E0={0}

Therefore, the eigenvalue and eigenvector is.位=0,E0={0}

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

Find a 2脳2matrix A such that [31]and [12] are eigenvectors of A , with eigenvalues 5 and 10 , respectively.

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

8((110022003)

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.

True or false? If the determinant of a 2 脳 2 matrix A is negative, then A has two distinct real eigenvalues.

Find a 2脳2matrixsuch that

X鈫�(t)=[2t-6t2t+6t]is a trajectory of the dynamical systemrole="math" localid="1659527385729" x鈫�(t+1)=Ax鈫�(t)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics 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.