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.

14 ft 7 inches

step-by-step explanation:

since each model inch corresponds to 25 real inches, 7 model inches will correspond to

7×25" = 175"

at 12" per foot, that is 14 feet, 7 inches.

16

step-by-step explanation: