1. Let D4₁: = {Po. P1, P2, P3, M1, M2, 81, 82} defined by the following: HIE 2 3 4 234 1234 2 1 4 3, Po 1 P1 = " " H₂= 1 2 3 4 234 1 2 3 4 4321 " " P₂ = 8₁ = 1 2 3 3412 1 2 3 4 3214 4) " P3 = 8₂ = 1234 4123 123 1432 (a) Find all left cosets of {po, 2}. (b) Repeat the preceding exercise, but find the right cosets this time. Are they the same as the left cosets?
1. Let D4₁: = {Po. P1, P2, P3, M1, M2, 81, 82} defined by the following: HIE 2 3 4 234 1234 2 1 4 3, Po 1 P1 = " " H₂= 1 2 3 4 234 1 2 3 4 4321 " " P₂ = 8₁ = 1 2 3 3412 1 2 3 4 3214 4) " P3 = 8₂ = 1234 4123 123 1432 (a) Find all left cosets of {po, 2}. (b) Repeat the preceding exercise, but find the right cosets this time. Are they the same as the left cosets?
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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Transcribed Image Text:1. Let D₁ = {po. P1, P2, P3, M1, M2, 81, 82} defined by the following:
1 2 3 4
2 3 4 1
1 2 3 4
3412
1 2 3 4
3214
PO
14
2 3 4
2
3 4
1234
(3)
2 1 4 3,
1
P1 =
H₂ =
1 2 3 4
4 3 2 1,
"
2
P2 =
d₁ =
2
2
P3 =
d₂ =
1
4
1
1
2 3 4
1 2 3
2 3 4
432
(a) Find all left cosets of {po, 2}.
(b) Repeat the preceding exercise, but find the right cosets this time. Are they the same as the
left cosets?
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