Let (x, y) E R × R. Consider the following functions from R? to R? r(х, у)) %3D (-у, х) and s(x, y)) = (x,-y). (a) What is the order of r? of s? Justify. Note: r" = r ororo….or. n times (b) Let f be of the form r's' where 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let (x, y) E R × R. Consider the following functions from R? to R?
r(х, у)) %3D (-у, х)
and s(x, y)) = (x,-y).
(a) What is the order of r? of s? Justify. Note: r" = r ororo….or.
n times
(b) Let f be of the form r's' where 0<i s \r| and 0 <j< \sl. Fill in the table with these distinct functions
and their images.
image of
(х, у)
f
i
(x, y)
(-у, х)
(x, -y)
It may be nice to enumerate the elements alphabetically, e.g. list rs ahead of r²s.
(c) Draw the point P(x, y) on quadrant I of the real plane. Show the image of P under each function f except
for the identity i.
...
Transcribed Image Text:Let (x, y) E R × R. Consider the following functions from R? to R? r(х, у)) %3D (-у, х) and s(x, y)) = (x,-y). (a) What is the order of r? of s? Justify. Note: r" = r ororo….or. n times (b) Let f be of the form r's' where 0<i s \r| and 0 <j< \sl. Fill in the table with these distinct functions and their images. image of (х, у) f i (x, y) (-у, х) (x, -y) It may be nice to enumerate the elements alphabetically, e.g. list rs ahead of r²s. (c) Draw the point P(x, y) on quadrant I of the real plane. Show the image of P under each function f except for the identity i. ...
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