Consider R+ the set of all positive real numbers (here zero is not positive) equipped with the following operations: (i) u ⊕ v = uv, for any u, v ∈ R+ (ii) α ⊙ u = uα, for any α ∈ R and any u ∈ R+. show that R+ is a vector space (check the closure under the operations ⊕ and ⊙ and the 8 axioms).

Consider R+ the set of all positive real numbers (here zero is not positive) equipped with the following operations: (i) u ⊕ v = uv, for any u, v ∈ R+ (ii) α ⊙ u = uα, for any α ∈ R and any u ∈ R+. show that R+ is a vector space (check the closure under the operations ⊕ and ⊙ and the 8 axioms).

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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Question

Consider R⁺ the set of all positive real numbers (here zero is not positive) equipped with the following operations:

(i) u ⊕ v = uv, for any u, v ∈ R⁺

(ii) α ⊙ u = u^α, for any α ∈ R and any u ∈ R⁺.

show that R⁺ is a vector space (check the closure under the operations ⊕ and ⊙ and the 8 axioms).

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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