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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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