Arizona State University (ASU) MAT343 Applied Linear Algebra Exam 2 Practice

Question: 1 / 400

Which of the following is not one of the axioms that define a vector space?

Closure under addition

Existence of a zero vector

Existence of a maximum vector

A vector space is defined by a set of axioms that specify the properties of addition and scalar multiplication that must hold for the elements within that space. The axioms include closure under addition, which means that the sum of any two vectors in the space must also be a vector in that space. The existence of a zero vector is another axiom that states there must be a vector in the space such that when it is added to any vector, it leaves that vector unchanged. Additionally, the concept of additive inverses is essential; for each vector in the space, there must be another vector (its inverse) that, when added together, results in the zero vector.

The notion of a maximum vector, however, is not included in the axioms defining a vector space. A maximum vector would imply some form of order or hierarchy among vectors, which does not align with the structure of a vector space as defined by standard linear algebra. Thus, this characteristic is not a requirement or part of the definition of a vector space.

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Existence of additive inverses

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