Detemine whether the set, M, with the standard operations, is a vector space. Ifit is not, then detemine the set of axioms that it fails. a) This set is not a vector space. It fails the following axioms. Commutative property Additive identity Distributive property b) This set is not a vector space. It fails the following axioms. Scalaridentity Associative property . Distributive property Additive identity c) This set is a vector space. All ten vector space axioms hold. d) This set is not a vector space. It fails the following axioms. Additive identity Additive inverse Associative property Scalaridentity
Detemine whether the set, M, with the standard operations, is a vector space. Ifit is not, then detemine the set of axioms that it fails. a) This set is not a vector space. It fails the following axioms. Commutative property Additive identity Distributive property b) This set is not a vector space. It fails the following axioms. Scalaridentity Associative property . Distributive property Additive identity c) This set is a vector space. All ten vector space axioms hold. d) This set is not a vector space. It fails the following axioms. Additive identity Additive inverse Associative property Scalaridentity
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:Detemine whether the set, M,, with the standard operations, is a vector space. Ifit is not, then detemine
the set of axioms that it fails.
This set is not a vector space. It fails the following axioms.
Commutative property
Additive identity
Distributive property
b)
a)
This set is not a vector space. It fails the following axioms.
Scalaridentity
Associative property
Distibutive property
Additive identity
c)
This set is a vector space. All ten vector space axioms hold.
This set is not a vector space. It fails the following axioms.
d)
Additive identity
Additive inverse
Associative property
Scalaridentity
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