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B A Figure 1: Equilateral triangle (a) (b) (c) C 3. An Abelian Group? Consider the equilateral triangle AABC as below Denote by D3 the set of all transformations such as reflection, rotation, that leave the shape and position of this triangle fixed. • We define Ra to be the counter-clockwise rotation by a around the center of the triangle. We define FA to be the reflection across the line that passes A and bisects BC, similarly for FB and Fc. . Moreover for a, b = D3, "a+b" is defined as the composition a o b (b first, then a). What is R2 + FA? What is FA+ FB? List all elements of D3 (No proof needed).

B A Figure 1: Equilateral triangle (a) (b) (c) C 3. An Abelian Group? Consider the equilateral triangle AABC as below Denote by D3 the set of all transformations such as reflection, rotation, that leave the shape and position of this triangle fixed. • We define Ra to be the counter-clockwise rotation by a around the center of the triangle. We define FA to be the reflection across the line that passes A and bisects BC, similarly for FB and Fc. . Moreover for a, b = D3, "a+b" is defined as the composition a o b (b first, then a). What is R2 + FA? What is FA+ FB? List all elements of D3 (No proof needed).

Advanced Engineering Mathematics
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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[Classical Geometries] How do you solve this question? write neatly Thank you

B A Figure 1: Equilateral triangle (a) (b) (c) (d) C 3. An Abelian Group? Consider the equilateral triangle AABC as below Denote by D3 the set of all transformations such as reflection, rotation, that leave the shape and position of this triangle fixed. • We define Ra to be the counter-clockwise rotation by a around the center of the triangle. We define FA to be the reflection across the line that passes A and bisects BC, similarly for FB and Fc. . Moreover for a, b = D3, "a+b" is defined as the composition a o b (b first, then a). What is R2 +FA? What is FA+ FB? List all elements of D3 (No proof needed). Is D3 an Abelian group? Explain your answer.
Transcribed Image Text:B A Figure 1: Equilateral triangle (a) (b) (c) (d) C 3. An Abelian Group? Consider the equilateral triangle AABC as below Denote by D3 the set of all transformations such as reflection, rotation, that leave the shape and position of this triangle fixed. • We define Ra to be the counter-clockwise rotation by a around the center of the triangle. We define FA to be the reflection across the line that passes A and bisects BC, similarly for FB and Fc. . Moreover for a, b = D3, "a+b" is defined as the composition a o b (b first, then a). What is R2 +FA? What is FA+ FB? List all elements of D3 (No proof needed). Is D3 an Abelian group? Explain your answer.
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