To find a basis for the subspace of R^4 spanned by the set S, the first step is to determine if the vectors in S are linearly independent. If they are independent, they form a basis for a 4-dimensional subspace. If not, one vector can be removed, and the process should be repeated with the remaining vectors. This method ensures that the resulting set of vectors will still span the same subspace while maintaining linear independence. Ultimately, identifying a basis involves careful analysis of the linear relationships among the vectors in S.
