Question: (a) Give an example of a matrix A such that A2 has an eigenvector that is not an eigenvector of A. (b) Show that, in

(a) Give an example of a matrix A such that A2 has an eigenvector that is not an eigenvector of A.
(b) Show that, in general, every eigenvalue of A2 is the square of an eigenvalue of A.

Step by Step Solution

★★★★★

3.33 Rating (177 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Let Then e 2 is an eigenvector of A 2 O but is not an eigenvector of A b Suppose A S J S 1 ... 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)

952-M-L-A-E (2725).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

A matrix A is idempotent if A2 = A. Show that the only possible eigenvalues of an idempotent matrix are = 0 and = 1. Then give an example of a matrix that is idempotent and has both of these two...

Give an example of a matrix with a left inverse, but not a right inverse. Is your left inverse unique?

(a) Show that, for any square matrix A, AT and A have the same characteristic polynomial and hence the same eigenvalues. (b) Give an example of a 2 2 matrix A for which AT and A have different...

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...

Can you please help me with number 12 and number 15. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! 5.7 Matrix Exponentials...

Can you please help me with number 31. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! 5.7 Matrix Exponentials and Linear...

Can you please help me with number 12 and number 15. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! 5.6 Problems Find...

Can you please help me with number 21. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! Open with Chapter 5 Linear Systems...

Can you please help me with number 15. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! Linear Systems quations 406 The...

I'm stuck in the question solve this question quickly 5. The next problems di5cuss eigenvalues and eigenvectors ofstochastic matriCes. Stochastic matrices are very useful for ranking sport teams or...

When the tension is 402 N, what is the tensile stress in the piano wire in Problem 84? How does that compare to the elastic limit of steel piano wire (8.26 108 Pa)?

Find the net income of Turbo Start (prob. 17-17) given the following data from the balance sheet and income statement. Turbo Start Data ($1000s) Accounts payable...

Choose one of the following 3 topics for your lab project: Package Delivery Service Software - A competitor to UPS, FedEx, or DHL that delivers packages internationally Zoo Management System Software...

Recall from previous economics courses the notion of a production possibilities curve. Draw such a curve for two goods such that it is concave to origin. Explain the concept of the marginal rate of...

The graph shown gives a salesmans distance from his home as a function of time on a certain day. Describe in words what the graph indicates about his travels on this day. Distance from home (miles)...

You put some ice cubes in a glass, fill the glass with cold water, and then let the glass sit on a table. Describe how the temperature of the water changes as time passes. Then sketch a rough graph...

Sketch a rough graph of the number of hours of daylight as a function of the time of year.

2. Operations are performed on eight machines as follows: 1. Face: lathe #609 2. Drill-Tap: machine #501 3. Drill: machine #101 4. Tap: machine #301 5. Drill: machine #102 6. Tap: machine #302 7....

Exercise 9-4 Prepare a Flexible Budget Performance Report [LO9-4] Vulcan Flyovers offers scenic overflights of Mount St. Helens, the volcano in Washington State that explosively erupted in 1982. Data...

The Retained earnings account has a credit balance of $47,000 before closing entries are made. Total revenues for the period are $65,200, total expenses are $44,800, and dividends are $13,000. What...