Define an equivalence relation on R² by: ¤1, Y1) ~ (x2, Y2) e if and only if (*1, Yı) and (x2, Y2) have the same distance from the origin. (a) Interpret the equivalence classes geometrically and describe the quotient R²/ ~. (b) Is the function f: (R°/ ~) → R, [(21, yn)] → 국+ yf well defined?
Define an equivalence relation on R² by: ¤1, Y1) ~ (x2, Y2) e if and only if (*1, Yı) and (x2, Y2) have the same distance from the origin. (a) Interpret the equivalence classes geometrically and describe the quotient R²/ ~. (b) Is the function f: (R°/ ~) → R, [(21, yn)] → 국+ yf well defined?
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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![Define an equivalence relation on R² by:
¤1, Y1) ~ (x2, Y2) E if and only if (x1, Y1) and (x2, Y2) have the same distance from the origin.
(a) Interpret the equivalence classes geometrically and describe the quotient R?/ ~.
(b) Is the function
f: (R²/ ~) → R, [(x1,y1)] → xỉ + yỉ
well defined?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c99a240-9de7-4947-9b54-53ff2cf6c85e%2Fcfb28f9f-40b4-4540-b456-6b43248d5e0f%2F5zbs7io_processed.png&w=3840&q=75)
Transcribed Image Text:Define an equivalence relation on R² by:
¤1, Y1) ~ (x2, Y2) E if and only if (x1, Y1) and (x2, Y2) have the same distance from the origin.
(a) Interpret the equivalence classes geometrically and describe the quotient R?/ ~.
(b) Is the function
f: (R²/ ~) → R, [(x1,y1)] → xỉ + yỉ
well defined?
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