Determine if the described set is a subspace. The subset of R2 consisting of vectors of the form a b , where a and b are rational numbers. The set is a subspace. The set is not a subspace. If so, give a proof. If not, explain why not.

Yes, W is a subspace.

Step-by-step explanation:

Let V be a vector space and W be a subset of V.

W is said to be a subspace of the vector space V if it satisfies the following conditions:

1. W is non-empty.

2. If then

3. If then where k is a scalar.

Solution:

Let

Here, Q denotes the set of rational numbers.

W is non-empty as being a rational number.

Let where a, b, c, d are rational numbers.

as ab + cd is a rational number being the sum and product of rational numbers.

Let and k be a scalar

being the product of rational numbers a and b.

Therefore, W is a subspace as it satisfies all the conditions.