Let us define a relation S on R3: If p1 = (x1, y1, z1) and p2 = (x2, y2, z2) are two points in R3, then (p1, p2) in S (or p1 ~ p2) if (x1 - x2) + 2(y1 - y2) + 3(z1 - z2) = 0. Describe all equivalence classes.

Let us define a relation S on R3: If p1 = (x1, y1, z1) and p2 = (x2, y2, z2) are two points in R3, then (p1, p2) in S (or p1 ~ p2) if (x1 - x2) + 2(y1 - y2) + 3(z1 - z2) = 0. Describe all equivalence classes.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 12E: Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and...

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Let us define a relation S on R³: If p₁ = (x₁, y₁, z₁) and p₂ = (x₂, y₂, z₂) are two points in R³, then (p₁, p₂) in S (or p₁ ~ p₂) if (x₁ - x₂) + 2(y₁ - y₂) + 3(z₁ - z₂) = 0.

Describe all equivalence classes.

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