The group D4 of symmetries of a square is given by D4 = {I, R, R², R³, H, V, D, D'} where I is the identity, R is a clockwise rotation through 7/2, H and V are reflections in the horizontal and vertical, and D, D' are reflections in the diagonals y = x and y = -x respectively. [Hint: Don't do 64 calculations! First fill in the first row and column. The top left-hand 4 x 4 corner, and the main diagonal, are also quite easy. Then choose two or three other entries to do, and fill in the rest using the Latin square property. It's like doing a Sudoku!]

The group D4 of symmetries of a square is given by D4 = {I, R, R², R³, H, V, D, D'} where I is the identity, R is a clockwise rotation through 7/2, H and V are reflections in the horizontal and vertical, and D, D' are reflections in the diagonals y = x and y = -x respectively. [Hint: Don't do 64 calculations! First fill in the first row and column. The top left-hand 4 x 4 corner, and the main diagonal, are also quite easy. Then choose two or three other entries to do, and fill in the rest using the Latin square property. It's like doing a Sudoku!]

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.CR: Review Exercises

Problem 29CR: Use the standard matrix for counterclockwise rotation in R2 to rotate the triangle with vertices...

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Similar questions

Show that u and v in the figure at the right are equivalent.
Use the standard matrix for counterclockwise rotation in R2 to rotate the triangle with vertices (3,5), (5,3) and (3,0) counterclockwise 90 about the origin. Graph the triangles.

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