Let S' = {x € R² : ||x|| = 1} C X. and endow S' with the same equivalence (b) relation - as above. Describe the set S'/ - of equivalence classes of s' induced by . %3D
Let S' = {x € R² : ||x|| = 1} C X. and endow S' with the same equivalence (b) relation - as above. Describe the set S'/ - of equivalence classes of s' induced by . %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
answer b only
![2. Let X = R? - (0.0) and - be defined over X by setting
x -y = y = tx
for some non-zerol E R.
(a)
classes of X induced by -.
Prove that - is an equivalence relation on X and describe the set X/ ~ of equivalence
Let S' = {x € R? : ||x|| = 1} C X, and endow S' with the same equivalence
(ь)
relation - as above. Describe the set S'/~ of equivalence classes of S' induced by v.
(c)
element of the equivalence class with respect to the dictionary order. Sketch a graph of all the
representative points of all equivalence classes of S'/~.
Given a equivalence class [r] € S'/ ~, choose its representative r to be the largest](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47d4f3e4-a83c-4f8d-b768-34b8f144d14c%2F7123da86-544b-4601-b00e-f2b3fdade589%2Ft0e9gyw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let X = R? - (0.0) and - be defined over X by setting
x -y = y = tx
for some non-zerol E R.
(a)
classes of X induced by -.
Prove that - is an equivalence relation on X and describe the set X/ ~ of equivalence
Let S' = {x € R? : ||x|| = 1} C X, and endow S' with the same equivalence
(ь)
relation - as above. Describe the set S'/~ of equivalence classes of S' induced by v.
(c)
element of the equivalence class with respect to the dictionary order. Sketch a graph of all the
representative points of all equivalence classes of S'/~.
Given a equivalence class [r] € S'/ ~, choose its representative r to be the largest
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