Sets play an important role in mathematics. The set of natural numbers is represented by N. When something belongs to a set or is a member of the set we say that it is in the set or that the set contains it. For example 1,2, and 3 are natural numbers and thus are in N. Similarly, we can say that N contains 1,2, and 3.

R2,R3,andRn are also sets. [12] is in R2, [115]is in R3, and all vectors with n real numbers are in Rn.

Suppose uandv are two vectors inR3. (You don't know the specific entries of uandv.)

1. What vectors are in Span{u,v}? Describe the set.

2. Is u contained in Span{u,v}?

3. Is 2uv in Span{u,v}?

4. Is it possible that Span{u,v}=R3?

5. Give an example of a vector in Span{u,v} not already listed.