If A is diagonalizable, show that each of the following is also diagonalizable. (a) kA, k any

Question:

If A is diagonalizable, show that each of the following is also diagonalizable.
(a) kA, k any scalar.
(b) U-1AU for any invertible matrix U.

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra With Applications

ISBN: 9780070985100

7th Edition

Authors: W. Keith Nicholson

See More Books

Question Posted: Jun 21, 2016 06:33 AM

See More Questions

Show that each of the following matrices is nonsingular but not diagonalizable. a. b. c. d. 003 3 6-43 332 120 012 0
Show that each of these is diagonalizable. (a) (b) x,y,z scalars 1 1
Show that each of the following transition matrices reaches a state of equilibrium? (a) (b) (c) (d) 0.4 0.2 0.6 0.8 5 100 0.3 0.1 0.4 0.2 0.4 0.0 0.5 0.5 0.6
A common stock pays an annual dividend that increases by 4% annually and sells for $35 per share. If the market rate of return on this stock is 8%. What is the amount of the ?last dividend paid $1.53...
What is meant by using bases for setting a preliminary judgment about materiality? How will those bases differ for the audit of a manufacturing company and a government unit such as a school district?
What are the advantages and disadvantages of open and closed internal recruitment? LO7
What do you see as the advantages and disadvantages of breaking up Microsoft? LO.1
How does the strategic plan influence preparation of the master budget?
Glassworks Inc. produces two types of glass shelving, rounded edge and squared edge, on the same production line. For the current period, the company reports the following data. Direct materials...
Burger King is a US-based fast food restaurant chain. Burger King advertises, develops new foods, and procures ingredients, but it owns almost none of the actual restaurants. Instead, the restaurants...
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...
Give an example of two diagonalizable matrices A and B whose sum A + B is not diagonalizable.
Explain the purpose of a Pareto Chart. Give an example of when one would be used.
Joint Ventures are a common Mode of Entry in international business. Appreciate if in-depth elaboration provided on its advantages and disadvantages. Also briefly mention the factors which make joint...
The field excursion is intended to give students an opportunity to carry out an applied geographical research project based on observation, data recording, and analysis. Using a field site of your...
An angry coworker is expressing their needs through a rush of emotion and snide comments while another coworker is trying to interpret them to provide some help and support. You are a manager and...
You may have a general understanding of the difference between ethics and legality , but could you explain the distinction? It is not always easy to know where to draw the line between the two. Some...
Someone can be a good leader but not be a very good manager and vice-versa. Leadership is creating a vision for others to follow, establishing corporate values and ethics, and transforming the way...
What is the percent ionization of acetic acid, CH 3 COOH, in 1.0 M, 0.10 M, and 0.010 M CH 3 COOH?
Determine the reactions in supports A and D and connections B and C. Sketch its shear and moment diagram and determine the magnitude ankoration of the maximum shear and moment for every member. 18 3...
Show that ||A||F = ||AT||F.
Let A be a symmetric n n matrix. Show that ||A|| = ||A||1.
Let A be a 5 4 matrix with singular values 1 = 5, 2 = 3, and 3 = 4 = 1. Determine the values of ||A||2 and ||A||F.
*please calculate irr in excel
Which of the following would not be a period cost? Research and development Direct materials Office supplies Advertising costs
\ table [ [ Activity Cost Pool,Activity Measure,Total Cost,Total Activity ] , [ Machining , Machine - hours,$ 3 3 0 , 0 0 0 , 1 5 , 0 0 0 MHs ] , [ Machine setups,Number of setups,$ 3 0 0 , 0 0 0 , 5...

If A is diagonalizable, show that each of the following is also diagonalizable. (a) kA, k any

Question:

Step by Step Answer:

a Since A is diagonalizable let P 1 AP D be diagonal Then P 1 kAP ...View the full answer

Linear Algebra With Applications

Students also viewed these Linear Algebra questions