Final answer:
To identify a subspace of R4, the set must include the zero vector, be closed under vector addition, and be closed under scalar multiplication. Test each condition against the set to ascertain its subspace status.
Step-by-step explanation:
To determine which of the following sets is a subspace of R4, we need to use the criteria that define whether a subset V of a vector space is indeed a subspace. Specifically, a subspace must satisfy the following conditions: it must contain the zero vector, be closed under vector addition, and be closed under scalar multiplication. If you provide a specific set, we can check each of these conditions.
For a set to contain the zero vector, there must be an element (0, 0, 0, 0) in it. Closed under vector addition means that if you take any two vectors in the set and add them together, their sum must also be in the set. Closed under scalar multiplication means that if you take any vector in the set and multiply it by any scalar (a real number), the result should still be within the set.
We use these rules to test if the given set is a subspace of R4. For example, if the set contains tuples of real numbers (a, b, c, d) that form vectors in R4 and satisfies the above conditions, it is a subspace of R4.