Consider the vector space V = {v € R[v > 0} over F = R with the following operations of • (addition) vị + v2 = V1 · V2 for all vị and v2 in V , and • (scalar multiplication) a v = v° for all a € F and ve V. Answer the following questions. (a) if v1 = 2, v2 = 3 and a = 2, compute vi + V2 and a · V2. (b) Find the zero element 0 eV and then for each v e V find (-v) (additive inverse).

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Consider the vector space
V = {v € R[v > 0}
over F = R with the following operations of
• (addition) vị + v2 = V1 · V2 for all vị and v2 in V , and
• (scalar multiplication) a v = v° for all a € F and ve V.
Answer the following questions.
(a) if v1 = 2, v2 = 3 and a = 2, compute vi + V2 and a · V2.
(b) Find the zero element 0 eV and then for each v e V find (-v) (additive inverse).
Transcribed Image Text:Consider the vector space V = {v € R[v > 0} over F = R with the following operations of • (addition) vị + v2 = V1 · V2 for all vị and v2 in V , and • (scalar multiplication) a v = v° for all a € F and ve V. Answer the following questions. (a) if v1 = 2, v2 = 3 and a = 2, compute vi + V2 and a · V2. (b) Find the zero element 0 eV and then for each v e V find (-v) (additive inverse).
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