Using the 10 properties: (a) Show that the set of strictly positive reals: R+ = {a E R | a > 0}, provided with the operations defined below is a vector space: - Addition: a + b = ab for all a, b E R+ - Multiplication by a scalar: k*a=ak, for all k E R and a E R+ (b) Why is the set of positive reals { a E R | a ⩾ 0}, endowed with the same operations, not a vector space?
Using the 10 properties: (a) Show that the set of strictly positive reals: R+ = {a E R | a > 0}, provided with the operations defined below is a vector space: - Addition: a + b = ab for all a, b E R+ - Multiplication by a scalar: k*a=ak, for all k E R and a E R+ (b) Why is the set of positive reals { a E R | a ⩾ 0}, endowed with the same operations, not a vector space?
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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Using the 10 properties:
(a) Show that the set of strictly positive reals: R+ = {a E R | a > 0}, provided with the operations defined below is a
- Addition: a + b = ab for all a, b E R+
- Multiplication by a scalar: k*a=ak, for all k E R and a E R+
(b) Why is the set of positive reals { a E R | a ⩾ 0}, endowed with the same operations, not a vector space?
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