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A) Let f: R² R² be defined by k 0 f( = = 0 transformation u, where k is a scalar. The k f is called dilation if k> 1 and it is called contraction if 0

A) Let f: R² R² be defined by k 0 f( = = 0 transformation u, where k is a scalar. The k f is called dilation if k> 1 and it is called contraction if 0

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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A) Let f: R² R² be defined by 0 f(u) = [ko] 0 transformation f is called dilation if k> 1 and it is called contraction if 0 <k < 1. u, where k is a scalar. The Consider the rectangle R with the vertices (-2, 1), (-2,5), (4, 1), (4, 5). Suppose f is the dilation with k = 3. Find the image of R. Draw the rectangle R and its image on the xy-plane. B) Let f: R² R² be defined by 1 0 f(u) = [] u. The transformation f is called the reflection with respect to x-axis. Consider the triangle Twith the vertices (-1,-1), (2, 4), (5,2). Suppose f is the reflection with respect to x-axis. Find the image of T. Draw the triangle Tand its image on the xy- plane.
Transcribed Image Text:A) Let f: R² R² be defined by 0 f(u) = [ko] 0 transformation f is called dilation if k> 1 and it is called contraction if 0 <k < 1. u, where k is a scalar. The Consider the rectangle R with the vertices (-2, 1), (-2,5), (4, 1), (4, 5). Suppose f is the dilation with k = 3. Find the image of R. Draw the rectangle R and its image on the xy-plane. B) Let f: R² R² be defined by 1 0 f(u) = [] u. The transformation f is called the reflection with respect to x-axis. Consider the triangle Twith the vertices (-1,-1), (2, 4), (5,2). Suppose f is the reflection with respect to x-axis. Find the image of T. Draw the triangle Tand its image on the xy- plane.
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