Extracted text: Suppose W is a subspace of R" spanned by n nonzero orthogonal vectors. Explain why W = R. The goal is to show that the subspace W is actually all of R". In general, when are two subspaces known to be the same space? O A. Two subspaces are the same when they are spanned by the same vectors. O B. Two subspaces are the same when they have the same dimension. OC. Two subspaces are the same when one subspace is a subset of the other subspace. O D. Two subspaces are the same when they are subsets of the same space. To start, assume that W is a subspace of R" spanned by n orthogonal nonzero vectors. Call these vectors v,, v2, V3, ..., Vn. By assumption, W= Span (v,, v2, V3, ..., v. Which of the following statements follows immediately from the assumption that the vectors v,, V2, V3, ..., V, are orthogonal and nonzero? O A At least one element of (v1, V2, V3, ..., Vn is zero. O B. R" = Span(v1, v2, V3, .. Vn} Oc. {V1. V2. V3. .., Vn) is linearly dependent. O D. {V1. V2, V3, ..., Vn} is linearly independent. How does this show that W = R"? O A. The vectors v,, V2, V3 ., V, are in both W and R". O B. The column vectors v,, v2, V3, .., Vn span R" if and only if (v1, V2, V3, ..., Vn} is linearly dependent. O C. The column vectors v4, V2, V3, .., Vn span R" if and only if (v,, V2, V3, ..., V is linearly independent. O D. w= (v,, v2, V3, ..., Vn} = R".