Lucy is knitting a blanket and needs to buy some more yarn. At her local craft store, 2 skeins of yarn cost $7 and 8 Skeins of y
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Answer:
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:
- Conmutativity
- Associativity of addition and scalar multiplication
- Additive Identity
- Additive inverse
- Multiplicative Identity
- Distributive properties.
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.