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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