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(a) {(a1, a2, a3) E R³ | a1 + a2 = 0, a3 = 0}. (b) {(a1, a2, a3) ER³ | a2a3 = 0}. (c) {(a1, a2, a3) ER³ | a1 + a2 ≤ a3}. (d) {(a1, a2, a3) E R³ | a1 + a2+ a3 = 1}. (e) {(0,0,0)}.

(a) {(a1, a2, a3) E R³ | a1 + a2 = 0, a3 = 0}. (b) {(a1, a2, a3) ER³ | a2a3 = 0}. (c) {(a1, a2, a3) ER³ | a1 + a2 ≤ a3}. (d) {(a1, a2, a3) E R³ | a1 + a2+ a3 = 1}. (e) {(0,0,0)}.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 3E
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Question

Which of the listed subsets of the vector space R^3 is homogeneous but not additive?

(a) {(a1, a2, a3) E R³ | a1 + a2 = 0, a3 = 0}. (b) {(a1, a2, a3) ER³ | a2a3 = 0}. (c) {(a1, a2, a3) ER³ | a1 + a2 ≤ a3}. (d) {(a1, a2, a3) E R³ | a1 + a2+ a3 = 1}. (e) {(0,0,0)}.
Transcribed Image Text:(a) {(a1, a2, a3) E R³ | a1 + a2 = 0, a3 = 0}. (b) {(a1, a2, a3) ER³ | a2a3 = 0}. (c) {(a1, a2, a3) ER³ | a1 + a2 ≤ a3}. (d) {(a1, a2, a3) E R³ | a1 + a2+ a3 = 1}. (e) {(0,0,0)}.
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