Recall from Exercise 25 in section 5 4 that tr A (the trace of A) is the sum of the diagonal entries in A Show that the characteristic polynomial of A is Icirc raquo 2 (tr A) Icirc raquo det A Then show that the eigenvalues of a 2 x 2 matrix A are both real if and only if det Let A 21 all a12 d21 a22 422 s() tr A 2

Question: Recall from Exercise 25 in section 5.4 that tr A (the trace of A) is the sum of the diagonal entries in A. Show that

Recall from Exercise 25 in section 5.4 that tr A (the trace of A) is the sum of the diagonal entries in A. Show that the characteristic polynomial of A is
Î»2 - (tr A)Î» + det A

Then show that the eigenvalues of a 2 x 2 matrix A are both real if and only if det

Let A-[:21 = | all a12 d21 a22 422] s() tr A 2

Step by Step Solution

★★★★★

3.55 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The eigenvalues are both real if and only if ... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

922-L-A-E (382).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

In each case find the characteristic polynomial, eigenvalues, eigenvectors, and (if possible) an invertible matrix P such that P-1AP is diagonal. (a) (b) (c) (d) 2 -4 365 121 110 011 (h) A=10 10 1 -1...

For an n x n matrix A, the trace of A, Tr(A), is defined as the sum of the diagonal entries of A. Prove that the trace defines a linear transformation from Mnn to the vector space of all real numbers.

Use the result of Exercise 27 and the fact that /2 cos x dx = 1. (From Exercise 25 in Section 5.1), together with the properties of integrals, to evaluate /2 (2 cos x 5x) dx

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...

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

I'm in serious need of help in my accounting class (acc205) . I'm falling behind and I need help with this weeks assignment. for week three for the may-june month . can someone please help me ....

What is Exercise 32-45? I don't quite understand it, so I'm not sure if my work or answers are correct. Linear Algebra Lab Exercises Linear algebra deals with vectors and linear functions that act on...

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...

Suppose a person has a utility function given by U = [x + y]1/ where is a number between - and 1. This is called a constant elasticity of substitution (CES) utility function. You will encounter CES...

Suppose you begin year 1 with $5000. At the beginning of each year, you put half of your money under a mattress and invest the other half in Whitewater stock. During each year, there is a 50% chance...

A project's cash flow can be estimated as the project's operating cash flow blank

Reconsider the heat treating data from Table B.12 . Fit a model to the PITCH response using the variables x SOAKTIME SOAKPCT x DIFFTIME DIFFPCT 1 2 = = and as regressors. How does this model compare...

A and B are n n matrices. Justify each answer. (T/F) The matrices A and B -1 AB have the same sets of eigenvalues for every invertible matrix B.

Justify each answer. (T/F) An n n matrix with n linearly independent eigenvectors is invertible.

Verify the statements by providing justification for each statement. In each case, the matrices are square. If A is diagonalizable and B is similar to A, then B is also diagonalizable.

This term refers to losses arising from a government or state-owned-enterprise breaking or breaching of a business contract with the foreign private investor. A frequently cited cause of harm is...

Exercise 2-8 These financial statement items are for Sunland Company at year-end, July 31, 2017. Salaries and wages payable Salaries and wages expense Supplies expense Equipment Accounts payable...

Question 11 Not yet answered Marked out of 5.00 Flag question Different companies adopt different methods to evaluate their capital investment decision. Explain what is internal rate of return? Why...