Let A and B be n n idempotent matrices. (See Exercise 19.) (a) Show that AB
Question:
(a) Show that AB is idempotent if AB = BA.
(b) Show that if A is idempotent, then AT is idempotent.
(c) Is A + B idempotent? Justify your answer.
(d) Find all values of k for which k A is also idempotent.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (9 reviews)
We have A 2 A and B 2 B a AB 2 ABAB ABAB AABB since AB BA A 2 B 2 AB sin...View the full answer
Answered By
Qurat Ul Ain
Successful writing is about matching great style with top content. As an experienced freelance writer specialising in article writing and ghostwriting, I can provide you with that perfect combination, adapted to suit your needs.
I have written articles on subjects including history, management, and finance. Much of my work is ghost-writing, so I am used to adapting to someone else's preferred style and tone. I have post-graduate qualifications in history, teaching, and social science, as well as a management diploma, and so am well equipped to research and write in these areas.
4.80+
265+ Reviews
421+ Question Solved
Related Book For
Elementary Linear Algebra with Applications
ISBN: 978-0132296540
9th edition
Authors: Bernard Kolman, David Hill
Question Posted:
Students also viewed these Linear Algebra questions
-
Let A and B be n n matrices with eigenvalues and , respectively. (a) Give an example to show that + need not be an eigenvalue of A + B. (b) Give an example to show that need not be an eigenvalue...
-
Let A and B be n n matrices. Prove that the sum of all the eigenvalues of A + B is the sum of all the eigenvalues of A and B individually. Prove that the product of all the eigenvalues of AB is the...
-
Let A and B be n ( n orthogonal matrices. (a)Prove that A (AT + BT)B = A + B. (b)Use part (a) to prove that, if det A + det B = 0, then A + B is not invertible.
-
Accurate Job Costing must be done on three levels. Which of the following is not one of these levels? Tracking and controlling costs during jobs Tracking gross profit each month Filing records on...
-
Solve Problem 10-37 using QM for Windows. How many people, in total, will read or hear the advertisements?
-
Since diversification of funding sources seems so logical, why do some nonprofits resist going in this direction? How would you overcome this resistance?
-
You can find a 3 4 design with three levels of participation in after-school activities and four levels of GPA (1st, 2nd, 3rd, or 4th quartile). The outcome is success (as measured by peer rating) 4...
-
As operations manager of Holz Furniture, you must make a decision about adding a line of rustic furniture. In discussing the possibilities with your sales manager, Steve Gilbert, you decide that...
-
Assume a merchandising company provides the following information from its master budget for the month of May Sales $ 119,000 Cost of goods sold $ 84,000 Selling and administrative expenses $ 18,000...
-
Apple Corps Limited was founded in 1968 by members of the UK band, The Beatles John Lennon, Paul McCartney, George Harrison, and Ringo Starr. The corporation is privately- held by the four, 1968...
-
If A is an n n matrix, then A is called idempotent if A2 = A. (a) Verify that In and O are idempotent. (b) Find an idempotent matrix that is not In or O. (c) Prove that the only n n nonsingular...
-
Let A be an idempotent matrix. (a) Show that An = A for all integers n 1. (b) Show that In - A is also idempotent.
-
A Federation star ship (2.0 10 6 kg 2 ) uses its tractor beam to pull a shuttle craft (2.0 10 4 kg 2 ) aboard from a distance of 10 km away. The tractor beam exerts a constant force of 4.0 10 4 N...
-
We have five observations on \(x\) and \(y\). They are \(x_{i}=3,2,1,-1,0\) with corresponding \(y\) values \(y_{i}=4,2,3,1,0\). The fitted least squares line is \(\hat{y}_{i}=1.2+0.8 x_{i}\), the...
-
If you were to jump to the ground from a height of 2 meters, you'd likely injure yourself. But a pogo rider can do this repeatedly, bounce after bounce. How does the pogo stick make this possible? A....
-
Explain alternative methods for detecting unusual, extreme, or incorrect data values.
-
The owners of a motel discovered that a defective product was used during construction. It took seven months to correct the defects during which approximately 14 rooms in the 100 -unit motel were...
-
Define the elasticity of \(y\) with respect to \(x\) and explain its computation in the simple linear regression model when \(y\) and \(x\) are not transformed in any way, and when \(y\) and/or \(x\)...
-
Web-surfing exercise: Search the Web for a direct offering of a convertible preferred security. Possible search words include direct public offering or small corporate offering registration (SCOR)....
-
What key concerns must functional tactics address in marketing? Finance? POM? Personnel?
-
Find an equation for the plane spanned by the vectors u = (-1, 1, 1) and v = (3, 4, 4).
-
Use Theorem 5.2.4 to show that v1 = (1, 6, 4), v2 = (2, 4, -1), v3 = (-1, 2, 5), and w1 = (1, -2, -5), w2 = (0, 8, 9) span the same sub space of R3. Theorem 5.2.4 If S = {v1, v2,..., vr} and S' =...
-
Show that the following sets of functions are subspaces of F (-, ) (a) All everywhere continuous functions (b) All everywhere continuous functions that satisfy f + 2f = 0
-
sked byChina699 BEMIDJI STATE UNIVERSITY Department of Technology, Art & Design TADT 3217 : Materials Science & Metallurgy Hardness Testing [A continued look at the Heat Treatment of Steel] ...
-
1. Advocate Aurora Sheboygan Memorial Hospital health care product or service to be marketed in your community. 2. Conduct appropriate market research in your community to determine the demographics...
-
How do ethical leaders integrate ethical considerations into strategic decision-making processes, balancing short-term business objectives with long-term ethical imperatives to ensure sustainable...
Study smarter with the SolutionInn App