#14 on 3.1 on the picture I sent. po Thomas W. Hungerford - Abstrac XO File | C:/Users/angel/Downloads/Thomas%20W.%20Hungerford%20-%20Abstract%20Algebra_%20AN%20lntroduction-Cengage%20Learning%20(2014).pdf...Flash Player will no longer be supported after December 2020.Turn offLearn moreof 621-- A Read aloudV DrawF HighlightO Erase77(b) For any ring R, show that R* is a subring of R × R.Caprite 2012Cmpe laing A Righe Rad Mng sot be peanor d whete or in part De toonie dee, d perty com y bapma tBodk d . Btalntadd ty eda d dany a te oa gapei C Lang righto ddenal a g teit gt m i3.1 Definition and Examples of Rings5510. Is S= {(a, b)| a + b = 0} a subring of Z x Z? Justify your answer.11. Let S be the subset of M(R) consisting of all matrices of the form(a) Prove that S is a ring.G ) is a right identity in S (meaning that AJ = A for(b) Show that J =every A in S).(c) Show that Jis not a left identity in S by finding a matrix B in S such thatJB + B.For more information about S, see Exercise 41.12. Let Z[J denote the set {a + bi a, beZ}. Show that Z[] is a subring of C.13. Let Z[V2] denote the set {a + b21a, beZ}. Show that Z[V2] is a subringof R. See Example 20.]14. Let Tbe the ring in Example 8. Let S = {feT|f(2) = 0}. Prove that S is asubring of T.15. Write out the addition and multiplication tables for(a) Z, x Z;(b) Z, × Z,(c) Z, x Z,16. Let A =and 0 =in M(R). Let S be the set of all matrices Bsuch that AB = 0.(a) List three matrices in S. [Many correct answers are possible.](b) Prove that S is a subring of M(R). [Hint: If B and Care in S, show thatB + Cand BC are in S by computing A(B + C) and A(BC).]17. Define a new multiplication in Z by the rule: ab = 0 for all a, b,eZ Show thatwith ordinary addition and this new multiplication, Z is a commutative ring.18. Define a new multiplication in Z by the rule: ab = 1 for all a, b,EZ. Withordinary addition and this new multiplication, is Z is a ring?19. Let S = {a, b, c} and let P(S) be the set of all subsets of S; denote the

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To show that S=f∈T|f(2)=0 is a subring of the ring T of all the continuous real functions we must…

Answered: 14. Let Tbe the ring in Example 8.…

Math

Advanced Math

14. Let Tbe the ring in Example 8. LetS=SET|f{2) = 0f. Prove that Sis a subring of T.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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TION 18 Wholemark is an Internet order business that sells one popular New Year's greeting card once a year. The cost of the paper on which the card is printed is $0.05 per card, and the cost of printing is $0.15 per card. The company receives $2.15 per card sold. Since the cards have the current year printed on them, unsold cards have no salvage value. Its customers are from the four areas: Los Angeles, Santa Monica, Hollywood, and Pasadena. Based on past data, the number of customers from each of the four regions is normally distributed with a mean of 2,000 and a standard deviation 500. (Assume these four are independent.)What is the optimal production quantity for the card? (Use Excel's NORM.S.INV() function to find the z value. Round z value to 2 decimal places. Round your answer to the nearest whole number.)
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It has been suggested that daily production of a subassembly would be increased if better lighting were installed and background music and free coffee and doughnuts were provided during the day. Management agreed to try the scheme for a limited time. A listing of the number of subassemblies produced per week before and after the new work environment for each employee follows. Employee Past Production Record Production after Installing, Lighting, Music, etc. JD 23 33 SB 26 26 MD 24 30 RCF 17 25 MF 20 19 UHH 24 22 IB 30 29 WWJ 21 25 OP 25 22 CD 21 23 PA 16 17 RRT 20 15 AT 17 9 QQ 23 30 FIND: State the decision rule and show your work: Reject H0 if T ≤ : Compute T and arrive at a decision (Show your work). T = ____________ , do not reject H0.
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please help with 3, 4, and 5 High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants. Suppose that for a recent admissions class, an Ivy League college received 2851 applications for early admission. Of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. Answer questions 3-5. 3.Use the data to estimate P(E), P(R),…
Suppose the post office had 25 full-time employees andwas not allowed to hire or fire any employees. Formulate anLP that could be used to schedule the employees in order tomaximize the number of weekend days off received by theemployees.
Most railroad cars are owned by individual railroad companies. When a car leaves its home railroad's trackage, it becomes part of a national pool of cars and can be used by other railroads. The rules governing the use of these pooled cars are designed to eventually return the car to the home trackage. A particular railroad found that each month 60% of its boxcars on the home trackage left to join the national pool and 79% of its boxcars in the national pool were returned to the home trackage. If these percentages remain valid for a long period of time, what percentage of its boxcars can this railroad expect to have on its home trackage in the long run?
How is this set up