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.

answer: ur mum is gay

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)