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.
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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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d0d028c-3649-4645-9aa6-e7d2cc62dc7e%2F258d55bf-a3c5-4d83-bc1e-7b3cbdf57877%2F7b0qmhp_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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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