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Problem #1: Let V be the set of all ordered pairs of real numbers (u₁,u₂) with u2 > 0. Consider the following addition and scalar multiplication operations on u = (u₁, u₂) and v = = (v₁, v₂): u + v = (u₁ + v₁ +4,7u2v₂), ku = (ku1, ku₂) Use the above operations for the following parts. (a) Compute u + v for u = (-2, 3) and v = (-2,2). (b) If the set V satisfies Axiom 4 of a vector space (the existence of a zero vector), what would be the zero vector? (c) If u = (5,5), what would be the negative of the vector u referred to in Axiom 5 of a vector space? (Don't forget to use your answer to part (b) here!)

Problem #1: Let V be the set of all ordered pairs of real numbers (u₁,u₂) with u2 > 0. Consider the following addition and scalar multiplication operations on u = (u₁, u₂) and v = = (v₁, v₂): u + v = (u₁ + v₁ +4,7u2v₂), ku = (ku1, ku₂) Use the above operations for the following parts. (a) Compute u + v for u = (-2, 3) and v = (-2,2). (b) If the set V satisfies Axiom 4 of a vector space (the existence of a zero vector), what would be the zero vector? (c) If u = (5,5), what would be the negative of the vector u referred to in Axiom 5 of a vector space? (Don't forget to use your answer to part (b) here!)

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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Problem #1: Let V be the set of all ordered pairs of real numbers (µ₁, 42) with u₂ > 0. Consider the following addition and scalar multiplication operations on u = = (u₁, u₂) and v = (V₁, V2): u + v = (u₁ + v₁ + 4,7u2v2), ku = (ku1, ku2) Use the above operations for the following parts. (a) Compute u + v for u = (-2,3) and v = = (-2,2). (b) If the set V satisfies Axiom 4 of a vector space (the existence of a zero vector), what would be the zero vector? (c) If u = (5,5), what would be the negative of the vector u referred to in Axiom 5 of a vector space? (Don't forget to use your answer to part (b) here!)
Transcribed Image Text:Problem #1: Let V be the set of all ordered pairs of real numbers (µ₁, 42) with u₂ > 0. Consider the following addition and scalar multiplication operations on u = = (u₁, u₂) and v = (V₁, V2): u + v = (u₁ + v₁ + 4,7u2v2), ku = (ku1, ku2) Use the above operations for the following parts. (a) Compute u + v for u = (-2,3) and v = = (-2,2). (b) If the set V satisfies Axiom 4 of a vector space (the existence of a zero vector), what would be the zero vector? (c) If u = (5,5), what would be the negative of the vector u referred to in Axiom 5 of a vector space? (Don't forget to use your answer to part (b) here!)
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