Final answer:
The correct statement is that the set of linearly dependent vectors in R^n could but does not necessarily span R^n. Vector addition is commutative, meaning the sum of vectors does not depend on the order in which they are added.
Step-by-step explanation:
The best statement concerning the set S of linearly dependent vectors in Rn is A. The set S could, but does not have to, span Rn. A set of linearly dependent vectors means that there is a non-trivial combination of these vectors that equals the zero vector, implying at least one of the vectors can be written as a combination of the others. While linear dependence does not guarantee the set spans Rn, it is still possible for a set of linearly dependent vectors to span the entire space if the set contains enough vectors to cover all dimensions of Rn, despite the redundancy.
In general, in one dimension—as well as in higher dimensions—vector addition is a commutative operation. This means that the order of addition does not affect the sum of vectors. For example, for any three vectors A, B, and C with different lengths and directions, A + B + C will equal C + B + A or B + A + C, and so on. This property is a fundamental aspect of vector spaces.