Question

Why does this show that H is a subspace of R3? O A. The vector v spans both H and R3, making H a subspace of R3. OB. The span of any subset of R3 is equal to R3, which makes it a vector space. OC. It shows that H is closed under scalar multiplication, which is all that is required for a subset to be a vector space. OD. For any set of vectors in R3, the span of those vectors is a subspace of R3 O E. It shows that H contains the zero vector, which is all that is required for a subset to be a vector space. OF. The set H is the span of only one vector. If H was the span of two vectors, then it would not be a subspace of R3

Answer 1

Solution:

Option (E) is the correct answer. If any subset of  $\mathbb{R}^3$ contains the zero vector and forms a vectorspace, then it will be a subspace of  $\mathbb{R}^3$ . Since in option (E), H contains the zero vector ans which is all that ie required for a subset to be a vectorspace, so H is a subspace of  $\mathbb{R}^3$ .