Can you please show me how to write Z12? From the image, how did we get [8]12 = [20]12 .... rest is in the image. From where did the numbers come? 2. In Z7 , can you please show me how to get the multiplicative inverse of Z7 ? How did the book list [1]7-1 = [1]7 = [2]7-1 = [4]7
Can you please show me how to write Z12? From the image, how did we get [8]12 = [20]12 .... rest is in the image. From where did the numbers come? 2. In Z7 , can you please show me how to get the multiplicative inverse of Z7 ? How did the book list [1]7-1 = [1]7 = [2]7-1 = [4]7
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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Can you please show me how to write Z12?
From the image, how did we get [8]12 = [20]12 .... rest is in the image. From where did the numbers come?
2. In Z7 , can you please show me how to get the multiplicative inverse of Z7 ? How did the book list [1]7-1 = [1]7 = [2]7-1 = [4]7 .... the rest is in the image.
please do easily explain them to me so I can follow up with your steps and understand. Thank you.
![In Z7, each nonzero congruence class contains representatives which are rela-
tively prime to 7, and so each nonzero congruence class has a multiplicative inverse.
We can list them as [1]7' = [1]7, [2]7' = [4]7, [3]7'
We did not need to list [4],' and [5]7' since, in general, if [a],' = [b]n, then
[b],' = [a]n.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb708fa5-116d-42c3-bb62-31dd00678e29%2Fffd66daf-5f98-426d-9400-a712fe64e096%2F74lqfcg_processed.png&w=3840&q=75)
Transcribed Image Text:In Z7, each nonzero congruence class contains representatives which are rela-
tively prime to 7, and so each nonzero congruence class has a multiplicative inverse.
We can list them as [1]7' = [1]7, [2]7' = [4]7, [3]7'
We did not need to list [4],' and [5]7' since, in general, if [a],' = [b]n, then
[b],' = [a]n.
![In Z12, for example, we have [8]12
congruence classes gives the same answer, no matter which representatives we use:
[8]12 + [10]12 = [18]12 = [6]12 and also [20]12 + [34]12 = [54]12 = [6]12.
[20]12 and [10]12 = [34]12. Adding](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb708fa5-116d-42c3-bb62-31dd00678e29%2Fffd66daf-5f98-426d-9400-a712fe64e096%2Fknwkjqu_processed.png&w=3840&q=75)
Transcribed Image Text:In Z12, for example, we have [8]12
congruence classes gives the same answer, no matter which representatives we use:
[8]12 + [10]12 = [18]12 = [6]12 and also [20]12 + [34]12 = [54]12 = [6]12.
[20]12 and [10]12 = [34]12. Adding
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