Let h be the set of all polynomials having degree at most 4 and rational coefficients. determine whether h is a vector space. if it is not a vector space, determine which of the following properties it fails to satisfy. a: contains zero vector b: closed under vector addition c: closed under multiplication by scalars

Yes. It is a vector space over the field of rational numbers

Step-by-step explanation:

An element of the set has the form

where are rational coefficients.

The operations of addition and scalar multiplication are defined as follows:

The properties that , together the operations of vector addition and scalar multiplication,  must satisfy are:

This is not difficult with the definitions given. The most important part is to show that has a additive identity, which is the zero polynomial, that is closed under vector addition and scalar multiplication. This last properties comes from the fact that is a field, then it is closed under sum and multiplication.

1. 3

2. 4

3. 1

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-wfz

true

step-by-step explanation: