In the dihedral group D n , let R = R 360 / n and let F be any reflection.Write each of the following products in the form R i or R i F , where 0 ≤ i ≤ n . a. In D 4 , F R − 2 F R 5 b. In D 5 , R − 3 F R 4 F R − 2 c. In D 6 , F R 5 F R − 2 F
In the dihedral group D n , let R = R 360 / n and let F be any reflection.Write each of the following products in the form R i or R i F , where 0 ≤ i ≤ n . a. In D 4 , F R − 2 F R 5 b. In D 5 , R − 3 F R 4 F R − 2 c. In D 6 , F R 5 F R − 2 F
Solution Summary: The author explains the cardinality of D_4is 8, which is a group under composition of permutations.
In the dihedral group
D
n
, let
R
=
R
360
/
n
and let F be any reflection.Write each of the following products in the form
R
i
or
R
i
F
, where
0
≤
i
≤
n
. a. In
D
4
,
F
R
−
2
F
R
5
b. In
D
5
,
R
−
3
F
R
4
F
R
−
2
c. In
D
6
,
F
R
5
F
R
−
2
F
Use the dot product properties to evaluate each
expression in the left column and match its
corresponding answer in the right column.
Let u =(4, 5), v = (1, −6) and w=
V • W
u • (5v)
VW - u •
W
(2w) • u + v
v. (u - w)
:: -14 :: -64
L.
L.
:: 159
:: 130 :: -37
=(-7,-3).
11
-130
54
:: 59
:: -25
20a. Complete the rule for each reflection
1C.2 Please refer to the attached image for my question. Please show ALL your work. Thank you!
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