Determine whether the following set with the standard operations, is a vector space. If it is not, then determine the set of axioms that it fails. {(x, x,x): x is a real number} O a. This set is not a vector space. It fails the following axioms. Closer under addition Closer under scalar multiplication O b. This set is a vector space. All ten vector space axioms hold. O c. This set is not a vector space. It fails the following axioms. Commutative property Additive identity Distributive property O d. This set is not a vector space. It fails the following axioms. Scalar identity Associative property Distributive property Additive identity O e. This set is not a vector space. It fails the following axioms. Additive identity L Additive inverse Associaty pored with CamScanner Scalar identity
Determine whether the following set with the standard operations, is a vector space. If it is not, then determine the set of axioms that it fails. {(x, x,x): x is a real number} O a. This set is not a vector space. It fails the following axioms. Closer under addition Closer under scalar multiplication O b. This set is a vector space. All ten vector space axioms hold. O c. This set is not a vector space. It fails the following axioms. Commutative property Additive identity Distributive property O d. This set is not a vector space. It fails the following axioms. Scalar identity Associative property Distributive property Additive identity O e. This set is not a vector space. It fails the following axioms. Additive identity L Additive inverse Associaty pored with CamScanner Scalar identity
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:Determine whether the following set with the standard operations, is a vector space. If it is not, then determine the set of axioms that it fails.
{(x, x,x): x is a real number}
O a. This set is not a vector space. It fails the following axioms.
Closer under addition
Closer under scalar multiplication
O b. This set is a vector space. All ten vector space axioms hold.
O c. This set is not a vector space. It fails the following axioms.
Commutative property
Additive identity
Distributive property
O d. This set is not a vector space. It fails the following axioms.
Scalar identity
Associative property
Distributive property
Additive identity
O e. This set is not a vector space. It fails the following axioms.
Additive identity
L
Additive inverse
Accoriaty pred with CamScanner
Associative
Scalar identity
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