Are license requirements (in this problem) vectors?

Algebra Level pending

This problem’s question: {\color{#D61F06}\text{This problem's question: }} Are license requirements (in this problem) vectors?

An unnamed city requires every household to have a pet license of the appropriate type for each dog, cat, bird or reptile that the household has as a pet. The head of the household is responsible for acquiring the licenses. Pet shops can issue them on behalf of the city. The licenses are free and unlimited in quantity; but, any of these animal types without a license may be confiscated.

One is not required to have any pets. Negative licenses exist for some strange reason. One might talk about merging, separating or replicating households

Vectors have to be about numbers. only Yes No What do dogs, cats, etc.have to do with this?

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

The unit vectors are the pet types.

The scalar field is the integers.

Associativity and commutativity work as needed.

The identity element is a household without pets.

The negative licenses exist so that the scalar field can be all integers.

Compatibility with scalar multiplication works correctly.

Multiplication by the scalar 1 1 works correctly.

Distributivity of scalar multiplication with respect to vector addition works correctly.

Distributivity of scalar multiplication with respect to field addition works correctlly.

The vector space requirements are met.

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Deva Craig
Aug 20, 2019

We often like to think of vectors as "a quantity represented by an arrow with both a magnitude and direction". This definition by itself is actually for a very specific kind of vector, typically the physical type that represent some kind of motion or force. A more general definition for a vector would be "a quantity or object with more than one piece of information". In this case, the licenses have pieces of information such as the types of pet the house owner has and the number of licences that house would receive.

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