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5. Let a and b be real numbers, not both zero. For (71, y1) and (12, 42) in R², set (11, yı) ~ (12, y2) → a(11 – 12) + b(yı – y2) = 0. (a) Show that - defines an equivalence relation. (b) Identify the equivalence classes.

5. Let a and b be real numbers, not both zero. For (71, y1) and (12, 42) in R², set (11, yı) ~ (12, y2) → a(11 – 12) + b(yı – y2) = 0. (a) Show that - defines an equivalence relation. (b) Identify the equivalence classes.

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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5. Let a and b be real numbers, not both zero. For (71, y1) and (12, 42) in R², set (11, yı) ~ (12, y2) → a(11 – 12) + b(yı – y2) = 0. (a) Show that - defines an equivalence relation. (b) Identify the equivalence classes.
Transcribed Image Text:5. Let a and b be real numbers, not both zero. For (71, y1) and (12, 42) in R², set (11, yı) ~ (12, y2) → a(11 – 12) + b(yı – y2) = 0. (a) Show that - defines an equivalence relation. (b) Identify the equivalence classes.
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