Consider the four maps on R² given by Tix = Ax+b; for i = 1,2,3,4, where A = [ and the vectors b, are (0,0),(1,0), (0, 1), and (1,1). (a) Show that the fixed points of the 7's form the vertices of a square S. (b) Compute TS and T2S. (c) Use a computer to generate a picture of the fixed set.

Consider the four maps on R² given by Tix = Ax+b; for i = 1,2,3,4, where A = [ and the vectors b, are (0,0),(1,0), (0, 1), and (1,1). (a) Show that the fixed points of the 7's form the vertices of a square S. (b) Compute TS and T2S. (c) Use a computer to generate a picture of the fixed set.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 32E

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Question

H3.

C. Consider the four maps on R² given by T₁x = Ax+b; for i=1,2,3,4, where A = [0]
and the vectors b, are (0,0),(1,0), (0, 1), and (1,1).
(a) Show that the fixed points of the 7's form the vertices of a square S.
(b) Compute TS and T2S.
(c) Use a computer to generate a picture of the fixed set.

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