Question: Let (i). Write down necessary and sufficient conditions on the entries a, b, c, d that ensures that A has only real eigenvalues. (ii).Verify that

Let

a A = c d

(i). Write down necessary and sufficient conditions on the entries a, b, c, d that ensures that A has only real eigenvalues.

(ii).Verify that all symmetric 2 × 2 matrices satisfy your conditions.

(iii). Note down a non-symmetric matrix that full fill your conditions.

a A = c d

Step by Step Solution

★★★★★

3.52 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

i The characteristic equation p 2 a d ad bc 0 has real roots if ... View full answer

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

Document Format (1 attachment)

Word file Icon

952-M-L-A-E (2695).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Let (a) Write down necessary and sufficient conditions on the entries a, b, c, d that ensures that A has only real eigenvalues. (b) Verify that all symmetric 2 Ã 2 matrices satisfy your...

Q:

Consider the weighted inner product (v, w) = v1w1 + 1/2v2w2 + 1/3v3w3 on R3. (a) What are the conditions on the entries of a 3 3 matrix A in order that it be self-adjoint? (b) Write down an example...

Q:

Answer Exercise 7.5.12 for the inner product based on Exercise 7.5.12 Consider the weighted inner product (v, w) = v1w1 + 1/2v2w2 + 1/3v3w3 on R3. (a) What are the conditions on the entries of a 3...

Q:

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:...

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:

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

Q:

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

Q:

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:...

Q:

CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...

Q:

Prolog You are approached to compose a Prolog program to work with twofold trees. Your code shouldn't depend on any library predicates and you ought to expect that the mediator is running without...

Q:

For H2O, plot how the volume fraction, y, changes with quality, x, over the entire possible range at (a) p = 100 kPa (b) p = 20 MPa.

Q:

A) What is the payback period (in annual terms) of the following cashflow stream? Year 0: $-921.24 Year 2: $295.65 Year 8: $895.61 Year 10: $-238.36 Year 15: $949.73 Year 18: $-22.22 B) What is the...

Q:

Q1: What is a wave, and how is it categorized?

Q:

Suppose the relevant data for a no-government, no-foreign sector economy was as follows: (a) .25, (b) .1, and (c) equilibrium income in period 1 $600 billion. Use Domars model to determine the...

Q:

Consider the soil absorption data in Exercise 12-2. (a) Find a 95% confidence interval on the regression coefficient B1. (b) Find a 95% confidence interval on mean soil absorption index when x1 = 200...

Q:

Consider the NFL data in Exercise 12-4. (a) Find a 95% confidence interval on B8. (b) What is the estimated standard error of when x2 = 2000 yards, x7 = 60%, and x8 = 1800 yards? (c) Find a 95%...

Q:

Consider the gasoline mileage data in Exercise 12-5. (a) Find 99% confidence intervals on B1 and B6. (b) Find a 99% confidence interval on the mean of Y when x1 = 300 and x6 = 4. (c) Fit a new...

Q:

Calculatiag initial investment Vastine Medical. Inc.. is considering replacing its existing computer system, which was purchased 3 years ago at a cost ot $321,000. The system can be sold today for...

Q:

whats the answer ? Question 5 Weston Mnes has a cost of equity of 140 percent, a pretax cost of debt of 7.3 percent, and a return on assets of 12.6 percent. Ignore taxes What is the debt-equity...

Q:

1. How long will it take to save $15,000 by making deposits of $90 at the end of every month into an account earning interest at 4% compounded quarterly? (5 marks) 2. Compute the nominal annual rate...