Define T: R3 R3 by T(x) = Ax, where A is a 3 x 3 matrix

Question:

Define T: R3 → R3 by T(x) = Ax, where A is a 3 x 3 matrix with eigenvalues 5, 5, and -2. Does there exist a basis B for R3 such that the B-matrix for T is a diagonal matrix? Discuss.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra and Its Applications

ISBN: 978-0321791542

4th edition

Authors: David C. Lay

See More Books

Question Posted: May 02, 2016 12:06 PM

See More Questions

Define T: Pn Pn by T(p) = p(x) + xp'(x) for all p in Pn. Show that ker T = {0} and conclude that T is an isomorphism. [Write p(x) = a0 + a1x + + anxn and compare coefficients if p(x) = - xp'(x).]
Let A = {1, 2, 3}, B = {w, x, y, z}, and C = {4, 5, 6}. Define the relations R1 A B, R2 B C, and R3 B C, where R1 = {(1, w), (3, w), (2, x), (1, y)}, R2 = {(w, 5), (x, 6), (y, 4), (y, 6)}, and...
If X has hazard rate function X(t), compute the hazard rate function of aX where a is a positive constant.
Stock W, X and Y have expected returns of 9.0%, 16.1% and 11.3% respectively. Based on this and the attached information, what is the expected return of your portfolio? Stock W X Y Number of Shares...
A survey conducted by the Northwestern University Lindquist-Endicott Report asked 320 companies about the procedures they use in hiring. Only 54% of the responding companies review the applicant's...
Free-radical bromination of the following compound introduces bromine primarily at the benzylic position next to the aromatic ring. If the reaction stops at the monobromination stage, two...
How would you use workforce analytics to support talent programs such as recruiting, retention, and employee development?
David Roberts began an upholstery cleaning business on August 1 and engaged in the following transactions during the month: Aug. 1 Began business by depositing $30,000 in a bank account in the name...
Question 4 (8 Marks): For this question, your first task is to study the famous "Distance Vector (DV) Routing Algorithm" used at the network layer. You may refer to some slides I recently posted on...
You observe the following Treasury yields (all yields are shown on a bond equivalent basis): All the securities maturing from 1.5 years on are selling at par. The 0.5 and 1.0-year securities are...
In Exercises 13-16, define T: R2 R2 by T(x) = Ax. Find a basis B for R2 with the property that [T]B is diagonal. 1. 2. 4 0 2 3
Verify the statements in Exercises 1-2. The matrices are square. 1. If A is similar to B, then A2 is similar to B2. 2. If B is similar to A and C is similar to A, then B is similar to C.
Use the following information for Tipster Corporation to determine the 2010 and 2011 trend percents for net sales using 2010 as the baseyear. ($thousands) 2011 2010 Net sales ...$201,600 $114,800...
Is Dollar General expecting to benefit from economies of scale or does the firm think there are diseconomies of scale? Explain your answer. Discount grocer Dollar General has the Millennial shopper...
Why does economic growth destroy and create jobs?
Consider a building with 250 tons of peak cooling load. On a peak-cooling day, the cooling load occurs for 8 hours with a load factor of 75 percent. During the entire year, there are 1,000 equivalent...
Some parents refuse to get their children vaccinated against infectious diseases like measles and preventable infectious disease is returning to the developed world. A measles outbreak that began at...
Determine the simple payback period of installing a heat recovery system at a cost of $0.15/L/s for a 7,000/L/s makeup air system in a laboratory located in New York, New York. The indoor temperature...
Calculate dollar amounts accurate to the cent and percent amounts to three-figure accuracy. 150% of $60 is what amount?
Fred Farmer needs to prepare a balance sheet for his bank. He spent the day getting the following information. Fred needs your help to build a balance sheet and evaluate it. The information was...
V is a nonzero finite-dimensional vector space, and the vectors listed belong to V. Justify each answer. (T/F) If there exists a linearly dependent set {v 1 ,...,v p } in V, then dim V P.
Show that the given signal is a solution of the difference equation. Then find the general solution of that difference equation. Yk = 2k 4; Yk+2 + Yk+1 Yk = 1 + 3k -
Show that the given signal is a solution of the difference equation. Then find the general solution of that difference equation. Yk = 22k; Yk+22k+1 + 2yk = 2 + 3k
Do you envision the business as starting by targeting specific needs of a single target community (e.g. the target is San Francisco), targeting specific needs of a similar set of communities (e.g....
Define social media. ( 20 points ) How has social media changed the way marketers and consumers communicate with one another? Explain the implications for marketers. Describe how marketing managers...
Find an article or video offering advice on choosing the best financing option for a business. Answer the following questions: Which types of financing did they discuss? What advice did they offer?...

Define T: R3 R3 by T(x) = Ax, where A is a 3 x 3 matrix

Question:

Step by Step Answer:

If there is a basis B such that T B is diagonal then A i...View the full answer

Linear Algebra and Its Applications

Students also viewed these Linear Algebra questions