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2. Consider the set R>o endowed with operations and O defined as follows: a b:= a · b, co a := a°, for a, b e R>0 and e € R. Determine (with an argument) whether these operations make R»0 into a vector space over R, with O corresponding to addition and o corresponding to scalar multiplication. Here the notation a·b denotes the usual product of two (positive) real numbers, and aº denotes the usual exponential.

2. Consider the set R>o endowed with operations and O defined as follows: a b:= a · b, co a := a°, for a, b e R>0 and e € R. Determine (with an argument) whether these operations make R»0 into a vector space over R, with O corresponding to addition and o corresponding to scalar multiplication. Here the notation a·b denotes the usual product of two (positive) real numbers, and aº denotes the usual exponential.

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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2. Consider the set R>o endowed with operations e and o defined as follows: a e b:= a · b, co a := a°, for a, b e R>0 and c € R. Determine (with an argument) whether these operations make R>0 into a vector space over R, with e corresponding to addition and o corresponding to scalar multiplication. Here the notation a-b denotes the usual product of two (positive) real numbers, and aº denotes the usual exponential.
Transcribed Image Text:2. Consider the set R>o endowed with operations e and o defined as follows: a e b:= a · b, co a := a°, for a, b e R>0 and c € R. Determine (with an argument) whether these operations make R>0 into a vector space over R, with e corresponding to addition and o corresponding to scalar multiplication. Here the notation a-b denotes the usual product of two (positive) real numbers, and aº denotes the usual exponential.
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