2. (2 pts.) Let V be a five-dimensional vector space, and let S be a subset of V which is linearly independent. Complete the sentence by choosing exactly one of the following: Then S A) must have exactly five elements. B) must consist of at least five elements. C) must span V. D) must have at most five elements. E) must have infinitely many elements. F) can have any number of elements (except zero). G) must be a basis for V. 3. (2 pts.) Let V be a five-dimensional vector space, and let S be a subset of V which is linearly dependent. Complete the sentence by choosing exactly one of the following: Then S A) must have exactly five elements. B) must consist of at least five elements. C) must span V. D) must have at most five elements. E) must have infinitely many elements. F) can have any number of elements (except zero). G) must be a basis for V. H) None of A) through G) is correct. 4. (2 pts.) Let V be a three-dimensional vector space, and let S be a subset of V consisting of five vectors. Complete the sentence by choosing exactly one of the following: Then S A) can span V, but only if S is linearly independent, and vice versa. B) must be linearly dependent, and must span V. C) must be linearly dependent, but may or may not span V. D) may or may not be linearly independent, and may or may not span V. E) cannot span V, but can be linearly independent or dependent. F) must be linearly independent, but cannot span V. G) must be linearly independent, but may or may not span V. H) None of A) through G) is correct. 5. (1 pt.) Complete the sentence by choosing exactly one of the following options. The rank of a 3 x 5 matrix. A) must be zero. B) is three. C) can be any number from zero to five. D) can be any number from zero to two. E) can be any number from two to five. F) can be any number from zero to three. G) must be two. H) None of A) through G) is correct.