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e. Let X = R? – (0,0) and ~ be defined over X by setting X ~y + y = tx for some non-zero t € R. Let S' = {x € R² : ||x|| = 1} c X, and endow S' with the same equivalence above Describe the set S!Lo of equivalence classes of sl induced by %3D relation

e. Let X = R? – (0,0) and ~ be defined over X by setting X ~y + y = tx for some non-zero t € R. Let S' = {x € R² : ||x|| = 1} c X, and endow S' with the same equivalence above Describe the set S!Lo of equivalence classes of sl induced by %3D relation

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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2. Let X = R² – (0,0) and ~ be defined over X by setting x ~y + y = tx for some non-zero t e R. Let S' = {x € R? : ||x|| = 1}c X, and endow S' with the same equivalence relation - as above. Describe the set S'/ ~ of equivalence classes of S' induced by ~.
Transcribed Image Text:2. Let X = R² – (0,0) and ~ be defined over X by setting x ~y + y = tx for some non-zero t e R. Let S' = {x € R? : ||x|| = 1}c X, and endow S' with the same equivalence relation - as above. Describe the set S'/ ~ of equivalence classes of S' induced by ~.
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