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An affine transformation A(z): R² R² maps the "F"-shape on the left to the "F" on the right. (0, 1). (0,0) (0.-1) (1,1) (1,0) (-1,1) (0, 1) Z2 (-2,0) (-1.0) (0,0) (2) Give a 3 x 3 matrix that represents A over homogeneous coordinates. (b) Give a 3 x 3 matrix that represents A-¹ over homogeneous coordinates.

An affine transformation A(z): R² R² maps the "F"-shape on the left to the "F" on the right. (0, 1). (0,0) (0.-1) (1,1) (1,0) (-1,1) (0, 1) Z2 (-2,0) (-1.0) (0,0) (2) Give a 3 x 3 matrix that represents A over homogeneous coordinates. (b) Give a 3 x 3 matrix that represents A-¹ over homogeneous coordinates.

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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Question 1 An affine transformation A(z): R² R² maps the "F"-shape on the left to the "F" on the right.. (0, 1) (0,0) (0, -1) , (1, 1) (1,0) z (-1, 1) (0, 1) 22 (-2,0) (-1,0) (0,0) I (a) Give a 3 x 3 matrix that represents A over homogeneous coordinates. (b) Give a 3 x 3 matrix that represents A-¹ over homogeneous coordinates.
Transcribed Image Text:Question 1 An affine transformation A(z): R² R² maps the "F"-shape on the left to the "F" on the right.. (0, 1) (0,0) (0, -1) , (1, 1) (1,0) z (-1, 1) (0, 1) 22 (-2,0) (-1,0) (0,0) I (a) Give a 3 x 3 matrix that represents A over homogeneous coordinates. (b) Give a 3 x 3 matrix that represents A-¹ over homogeneous coordinates.
Expert Solution
Introduction

As per the question we are given an affine transform of a 2d object i.e. the letter "F" and from that we have to :

  1. Form the 3×3 transformation matrix A over homogenous coordinates {x  y, 1}
  2. Find the inverse of that transformation matrix i.e. A-1

 

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