Question: Construct the following examples (You must justify your examples): (a) Two matrices with the same characteristic polynomials x 2 (x 1) but not similar. (b)

Construct the following examples (You must justify your examples):

(a) Two matrices with the same characteristic polynomials x2(x 1) but not similar.

(b) A linear endomorphism T : R3 R3such that the characteristic polynomial of T is (x 1)(x + 1)2 and T2 =/ 1.

(c) Two 3 3 matrices A and B such that both A and B arediagonalizable but A + B is not diagonalizable.

(d) Two 3 3 matrices A and B such that both A and B arediagonalizable but AB is not diagonalizable.

(e) Four 2 2 matrices A1, A2, B1, B2 such that A1 B1 and A2 B2 but A1 + A2 / B1 + B2.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Q:

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Q:

%% Lab 2 - Your Name - MAT 275 Lab %% Example code % Example 1 % NOTE: Delete examples before submission. A = [1 0; 0 -1] A = [1, 0; 0, -1] % NOTE: The two matrices above are the same. We can...

Q:

This chapter presents students and early career executives with a sound understanding of theory. Theory is explored in terms of both anatomy (parts of the whole) and physiology (relationships with...

Q:

Hi, I need help with these questions. Write up your solution and results so that it could be understood by someone else completing the unit, including all required working, investigations and...

Q:

Developments in Technology Light is incident from air on the end face of a multimode optical fibre at angle of incidence as shown below. n n 1 2 The refractive indices of the core and cladding are...

Q:

Below are the questions: Below are the Header and Class file for problem number 2 1. (10 points) The price of an item that you want to buy is given by two integers as priceDollars dollars and...

Q:

,. solve the following Consider the following models describing the relationship between monthly return on the Standard & Poor's 500 stock market index (rsp500), the re- turn on three-month T-bills...

Q:

A. B. A. B. ( ( ) ) Beginning and Intermediate Algebra An open source (CC-BY) textbook Available for free download at: http://wallace.ccfaculty.org/book/book.html by Tyler Wallace 1 ISBN...

Q:

Suppose that there are three states of the world, a, b, and c. The probabilities of the three states are 1 = 0.25, 2 = 0.5, and 3 = 0.25. Let A, B, and C denote the Arrow-Debreu securities that pay...

Q:

Let (ɸ, I) be a smooth parametrization of some arc and Ï be a C1 function, 1-1 from J onto I, which satisfies Ï'(u) > 0 for all but finitely many u J. If Ï =...

Q:

Solve the initial value problems by using Laplace Transformation y'+y =8cost, y(0)=1. y'(0)=-1

Q:

Which of the following should be consideredwhen a company estimates the cash flows used to analyze a proposed project? Group of answer choices The new project is expected to reduce sales of one of...

Q:

2023 1040 form 1.Phillip and Claire are married and file a joint return. Phillip is self-employed as a real estate agent, and Claire is a flight attendant. Phillip and Claire have three dependent...