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 of all quadratic functions whose graphs pass through the origin with the standard operations 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. The set is not a vector space because the associative property of addition is not satisfied. The set is not a vector space because a scalar identity does not exist.

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 of all quadratic functions whose graphs pass through the origin with the standard operations 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. The set is not a vector space because the associative property of addition is not satisfied. The set is not a vector space because a scalar identity does not exist.

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 2EQ

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