227k views
2 votes
Find specific vectors u and v in w such that uv is not in w. This is enough to show that w is not a vector space. Two vectors in w, u and v, for which uv is not in w are:

User Smassey
by
7.7k points

1 Answer

5 votes

Final answer:

Without additional information regarding set w and how the product is defined for its vectors, specific vectors u and v cannot be provided to demonstrate that their product does not belong to set w, as required to show that w is not a vector space.

Step-by-step explanation:

The question refers to whether a set of vectors forms a vector space. It is a principle in linear algebra that in a vector space, the addition of any two vectors or the scalar multiplication of any vector must result in another vector that is also in that space. To prove that a set does not form a vector space, you can show that there exists at least one pair of vectors whose product (or addition, depending on the operation defined in the space) does not result in a vector in the same set.

In this particular case, we want to find two specific vectors, u and v, belonging to set w, such that the product of u and v (denoted as uv) does not result in a vector that is within set w. Unfortunately, without more information on how the product of two vectors is defined in this set or what set w precisely consists of, we cannot provide specific vectors u and v. Normally, a 'product' of vectors is not standard outside of certain contexts like the dot or cross product, which both have very specific definitions and properties in vector spaces.

User Basem
by
8.9k points