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...
What is the traditional financial performance measure for a cost center? A rev enue center?
Fever medication dosage. A pharmacist conducted an experiment to test the dosage of a new fever medicine FEVER needed to cure infants aged 612 months. They selected six infants who had about the same...
The following changes in account balances and other information for 2007 were taken from the accounting records of the Noble Company: Other information: Net income was $9,900. Dividends were declared...
Definitions (15 points): define and give an example (for each) 6) Asymmetric information 7) Physician induced demand 8) Community rating 9) QALY 10) Payers (payors)
Go to the Call Type by Rep worksheet. Tiana wants to compare the call data by type for each service rep. In cell A3, insert a PivotTable based on the Calls table. Use RepCalls as the name of the...
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.
Refer to problem 1. What would the standard deviation have to be for Tyler Apiaries to achieve Six Sigma quality levels with regard to the weight of the bee packages?
A parent acquires all of the stock of a subsidiary for $40 million in cash. The subsidiarys books report the following account balances at the date of acquisition (in trial balance format)....
1. Given: The sign for the Inn of the Prancing Pony in Bree-yes, it comes in pints-is fixed on the end of a beam of length 5L. If the sigh deflects too much then Gandalf will hit his head when he...
Q21) Add positive and negative charges as shown in the diagram below. Use the arrows of the simulation to guide you in drawing continuous electric field lines around and in between the three charges....
When 10.1 g CaO is dropped into a styrofoam coffee cup containing 157 g H2O at 18.0C, the temperature rises to 35.8C. Calculate the enthalpy change of the following reaction in kJ/mol CaO. Assume...
4-12. Sometimes heterogeneous chemical reactions take place at the walls of tubes in which reactive mixtures are flowing. If species A is being consumed at a tube wall because of a chemical reaction,...
In Problems 4951, write the resulting set using the listing method. {x|x is a positive integer and x! <100}
What are three disadvantages of using the direct write-off method?
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
The company sold merchandise to a customer on March 31, 2020, for $100,000. The customer paid with a promissory note that has a term of 18 months and an annual interest rate of 9%. The companys...
imer 2 0 2 4 Question 8 , PF 8 - 3 5 A ( similar to ) HW Score: 0 % , 0 of 1 0 0 points lework CH 8 Part 1 of 6 Points: 0 of 1 5 Save The comparative financial statements of Highland Cosmetic Supply...
An investor wants to purchase a zero coupon bond from Timberlake Industries today. The bond will mature in exactly 5.00 years with a redemption value of $1,000. The investor wants a 12.00% annual...

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