Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the ten vector space axioms that fails. The set {(x, y): x 2 0, y is a real number} The set is a vector space. O The set is not a vector space because it is not closed under addition. O The set is not a vector space because an additive identity does not exist. O The set is not a vector space because it is not closed under scalar multiplication. O The set is not a vector space because a scalar identity does not exist. Need Helpn? Read It
Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the ten vector space axioms that fails. The set {(x, y): x 2 0, y is a real number} The set is a vector space. O The set is not a vector space because it is not closed under addition. O The set is not a vector space because an additive identity does not exist. O The set is not a vector space because it is not closed under scalar multiplication. O The set is not a vector space because a scalar identity does not exist. Need Helpn? Read It
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 37E: Let V be the set of all positive real numbers. Determine whether V is a vector space with the...
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![Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the ten vector space axioms that fails.
The set
{(x, y): x > 0, y is a real number}
The set is a vector space.
The set is not a vector space because it is not closed under addition.
The set is not a vector space because an additive identity does not exist.
The set is not a vector space because it is not closed under scalar multiplication.
The set is not a vector space because a scalar identity does not exist.
Need Help?
Read It](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fb29e97-69ec-4648-a68a-3d3f1192ead8%2Fc695c473-d716-4466-b888-7e41ebc959cf%2Fj0v5mmk_processed.png&w=3840&q=75)
Transcribed Image Text:Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the ten vector space axioms that fails.
The set
{(x, y): x > 0, y is a real number}
The set is a vector space.
The set is not a vector space because it is not closed under addition.
The set is not a vector space because an additive identity does not exist.
The set is not a vector space because it is not closed under scalar multiplication.
The set is not a vector space because a scalar identity does not exist.
Need Help?
Read It
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