Question: By definition, A is idempotent if A2 = A, and B is nilpotent if Bm = 0 for some positive integer m. Give examples (different

By definition, A is idempotent if A2 = A, and B is nilpotent if Bm = 0 for some positive integer m. Give examples (different from 0 or I). Also give examples such that A2 = I (the unit matrix).

Step by Step Solution

★★★★★

3.38 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

J Idempotent are etc a... 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)

M-L-A-L-S (1).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...

Show that if An = O for some positive integer n (i.e., if A is a nilpotent matrix), then det(A) = 0.

Prove that if Ak = O for some positive integer k then 0 is the only eigenvalue of A?

solve these following 17. Show that 0 is the only nilpotent element in an integral domain. 18. A ring element a is called an idempotent if a2 = a. Prove that the only idempotents in an integral...

HW 12, MAT 312/AMS 351: SPRING 2017 Problem 1. (1) Set H = {4a + 6b | a, b Z} Z. Show that H is a subgroup of Z. (2) Is H cyclic? Problem 2. Write down all the cyclic subgroups of the following...

Please solve it as fast as possible. Abstract Algebra 9. Let R be the ring Z50- (a) (3 PTS) Find an element of R which is a zero-divisor. (b) (3 PTS) Find an element of R which is a unit. (c) (3 PTS)...

\fsh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Math 280 Strategies of Proof Fall 2007 Class Notes 3.6 Proving Conditional Statements II: Indirect Proofs In Section 3.4, we studied...

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

9/14/10 12:39 PM Page 381 Chapter dug84356_ch06a.qxd 6 Rational Expressions Advanced technical developments have made sports equipment faster, lighter, and more responsive to the human body. Behind...

Microkernel operating systems aim to address perceived modularity and reliability issues in traditional "monolithic" operating systems. (i) Describe the typical architecture of a microkernel...

On December 11, 2010, the Hooper Bank loans a customer $12,000 on a 60-day, 12% note. Required Prepare the journal entries necessary to record the receipt of the note by Hooper, the accrual of...

Explain, from a marketing perspective, why you would expect gross margin percentage, expenses-to-sales ratio, net profit margin, inventory turnover, and asset turnover to be different for a grocery...

Which of the following regulations establishes the SECs requirements for nonfinancial information disclosure? Multiple Choice Regulation 5 - K . Aeguietion 5 4 Requilation 5 - 4 Regulaticin 8 - 1...

Hypertension 1. Define hypertension using numerical values. 2. How does age affect the criteria for hypertension? 3. Differentiate between essential and secondary hypertension. 4. List conditions...

The following information was taken from Wicom's financial statements as of December 31, 2006. a. Calculate book value per share of common stock. b. Assume that the company also had $1,000,000 worth...

At the end of March Moore's Adjusted Trial Balance is as follows: Moore Transportation Service Adjusted Trial Balance January 31, 2017 ACCOUNT NAME DEBIT CREDIT Cash $13.332 Accounts Receivable...

Extra Hands Company has journalized the adjusting entries for the period ending December 31, 2018, and posted the adjustments to the following T-accounts. Using this data, prepare an adjusted trial...

Warsaw Bikes Inc. is a publicly traded Polish company that manufactures and sells bikes in Germany, Hungary and Poland. Country Currency Govt Bond Rate (in local currency) Govt Bond Rate (in Euros)...

Which of the following policy recommendations, if any, are consistent with the classical, Keynesian, monetarist, and/or modern consensus views of the macroeconomy? a. Since the long -run growth of...

State of Probability of Economy State of Economy Stock A Stock B Stock C Boom .30 .20 .25 .60 Normal .45 .15 .11 .05 Bust .25 .01 .15 .50 a-1. If your portfolio is invested 40 percent each in A and B...

The Campbell Company is considering adding a robotic paint sprayer to its production line. The sprayer's base price is $1,190,000, and it would cost another $16,500 to install it. The machine falls...

Internal rate of return For the project shown in the following table, , calculate the internal rate of retum (IRR). Then indicate, for the project, the maximum cost of capital that the firm could...