/*! 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} Q33E Show that if matrix A is similar... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q33E (page 346)

Show that if matrix A is similar to B, A-位濒n thenis similar toB-位濒n, for all scalars位.

Short Answer

Expert verified

The matrix is clearly implying B-位濒nis similar toA-位濒n

Step by step solution

01

Solving the matrix

Since A is similar to B, by definition, there exists a non-singular matrix

B=P-1AP

Therefore,

B-位濒n=P-1AP-位濒n=P-1AP-位笔-1Pln

02

Substitute I and P

HereP-1P=l and Pl=lP=P

=P-1AP-位笔-1lnP=P-1AP-P-1位濒nPB-位濒n=P-1A-位濒nP

Here, the final result is clearly implying B-位濒nis similar toA-位濒n

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.

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?

In all parts of this problem, let V be the linear space of all 2 脳 2 matrices for which [12]is an eigenvector.

(a) Find a basis of V and thus determine the dimension of V.

(b) Consider the linear transformation T (A) = A[12] from V to R2. Find a basis of the image of Tand a basis of the kernel of T. Determine the rank of T .

(c) Consider the linear transformation L(A) = A[13] from V to R2. Find a basis of the image of L and a basis of the kernel of L. Determine the rank of L.

Consider the matrix A=|abba|where aand bare arbitrary constants. Find all eigenvalues of A.

Find all2脳2matrices for whiche鈬赌1is an eigenvector.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.