16. Show that o(x) = 3x from Z12 to Z12 is a homomorphism. Let a, b E x 3(a + b) = 3a + 3b = p(a) + p(b) 17. Find the Ker o from Question 16. P(8) = 3 * 8 = 24 = 0 P(0) = 3 * 0 = 0 P(4) = 3 * 4 = 12 = 0 p(1) = 3 * 1 = 3 p(9) = 3 * 9 = 27 = 3 p(5) = 3 * 5 = 15 p(10) = 3 * 10 = 30 = 6 p(2) = 3 * 2 = 6 p(6) = 3 * 6 = 18 p(11) = 3 * 11 = 33 = 9 p(2) = 3 * 3 = 9 p(7) = 3 * 7 = 21 %3D Kernal ={[0],[4],[8]) 18. Find o(5) from Question 16.
16. Show that o(x) = 3x from Z12 to Z12 is a homomorphism. Let a, b E x 3(a + b) = 3a + 3b = p(a) + p(b) 17. Find the Ker o from Question 16. P(8) = 3 * 8 = 24 = 0 P(0) = 3 * 0 = 0 P(4) = 3 * 4 = 12 = 0 p(1) = 3 * 1 = 3 p(9) = 3 * 9 = 27 = 3 p(5) = 3 * 5 = 15 p(10) = 3 * 10 = 30 = 6 p(2) = 3 * 2 = 6 p(6) = 3 * 6 = 18 p(11) = 3 * 11 = 33 = 9 p(2) = 3 * 3 = 9 p(7) = 3 * 7 = 21 %3D Kernal ={[0],[4],[8]) 18. Find o(5) from Question 16.
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 need help with # 18 attached for abstract algebra plz. can u list steps clearly so I know how do do these inverses
![16. Show that o(x) = 3x from Z12 to Z12 is a homomorphism.
Let a, b E x
3(a + b) = 3a + 3b = p(a) + p(b)
17. Find the Ker o from Question 16.
P(8) = 3 * 8 = 24 = 0
P(0) = 3 * 0 = 0
P(4) = 3 * 4 = 12 = 0
p(1) = 3 * 1 = 3
p(9) = 3 * 9 = 27 = 3
p(5) = 3 * 5 = 15
p(10) = 3 * 10 = 30 = 6
p(2) = 3 * 2 = 6
p(6) = 3 * 6 = 18
p(11) = 3 * 11 = 33 = 9
p(2) = 3 * 3 = 9
p(7) = 3 * 7 = 21
%3D
Kernal ={[0],[4],[8])
18. Find o(5) from Question 16.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0548f28d-2867-4ce8-91e2-809a65372be3%2Ff57287b3-3b85-4e16-b9be-a3b60788e047%2Flqrjz6.png&w=3840&q=75)
Transcribed Image Text:16. Show that o(x) = 3x from Z12 to Z12 is a homomorphism.
Let a, b E x
3(a + b) = 3a + 3b = p(a) + p(b)
17. Find the Ker o from Question 16.
P(8) = 3 * 8 = 24 = 0
P(0) = 3 * 0 = 0
P(4) = 3 * 4 = 12 = 0
p(1) = 3 * 1 = 3
p(9) = 3 * 9 = 27 = 3
p(5) = 3 * 5 = 15
p(10) = 3 * 10 = 30 = 6
p(2) = 3 * 2 = 6
p(6) = 3 * 6 = 18
p(11) = 3 * 11 = 33 = 9
p(2) = 3 * 3 = 9
p(7) = 3 * 7 = 21
%3D
Kernal ={[0],[4],[8])
18. Find o(5) from Question 16.
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