Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails. The set ((x, y): *25, y 2.0) O 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 the commutative property of addition is not satisfied. O The set is not a vector space because the associative property of addition is not satisfied. O The set is not a vector space because it is not closed under scalar multiplication. Need Help? Watch H Read It

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.1: Vector Spaces And Subspaces
Problem 7EQ
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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
vector space axioms that fails.
The set
((x, y): x25, y 20)
O The set is a vector space.
The set is not a vector space because it is not closed under addition,
O The set is not a vector space because the commutative property of addition is not satisfied.
O The set is not a vector space because the associative property of addition is not satisfied.
O The set is not a vector space because it is not closed under scalar multiplication.
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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 vector space axioms that fails. The set ((x, y): x25, y 20) O The set is a vector space. The set is not a vector space because it is not closed under addition, O The set is not a vector space because the commutative property of addition is not satisfied. O The set is not a vector space because the associative property of addition is not satisfied. O The set is not a vector space because it is not closed under scalar multiplication. Need Help? Read It Watch
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