1 Let S be the set R². Define addition and multiplication operations on S as follows for all real numbers a, b, c, d, (a,b)+(c,d) := (a +c,b+d), (a,b) · (c,d) := (bd — ad — bc, ac — ad — bc). (a) Prove the right distributive law for S.
1 Let S be the set R². Define addition and multiplication operations on S as follows for all real numbers a, b, c, d, (a,b)+(c,d) := (a +c,b+d), (a,b) · (c,d) := (bd — ad — bc, ac — ad — bc). (a) Prove the right distributive law for S.
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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I’m sorry, I understand this is a 3 part questions but I’m really struggling on this and would be grateful if you could help. I don’t mind if your charge 3 questions, I just don’t know how I’d ask each question separately. Thank you very much
![1 Let S be the set R². Define addition and multiplication operations on S as follows
for all real numbers a, b, c, d,
(a,b)+(c,d) := (a +c,b+d),
(a,b) · (c,d) := (bd — ad — bc, ac — ad — bc).
(a) Prove the right distributive law for S.
(b) What is the multiplicative identity element for S? Explain how you found it.
(c) Using (b), prove the multiplicative identity law for S.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4082be17-8615-459e-878a-685f4f1bd2cd%2F6fa99149-aafa-476b-b803-ac337569a7e3%2F2ud6imtg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1 Let S be the set R². Define addition and multiplication operations on S as follows
for all real numbers a, b, c, d,
(a,b)+(c,d) := (a +c,b+d),
(a,b) · (c,d) := (bd — ad — bc, ac — ad — bc).
(a) Prove the right distributive law for S.
(b) What is the multiplicative identity element for S? Explain how you found it.
(c) Using (b), prove the multiplicative identity law for S.
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