Please verify my answers below are correct.

Determine whether each statement is True or False. Justify each answer. a. A vector is any element of a vector space. Is this statement true or false? O A. False; not all vectors are elements of a vector space. O B. False; a vector space is any element of a vector. O C. True by the definition of a vector space b. If u is a vector in a vector space V, then ( - 1)u is the same as the negative of u. Is this statement true or false? O A. False because for each u in V, there is a vector - u in V such that u + ( - u) = 0 O B. True because for each u in V, - u = ( - 1)u O C. True because for each u in V, there is a vector - u in V such that u + ( - u) = 0 O D. False because for each u in V, - u =u C. A vector space is also a subspace of itself. Is this statement true or false? A. False because the axioms for a vector space do not include all the conditions for being a subspace O B. False because the conditions for a subspace do not include all the axioms for being a vector space O C. True because the axioms for a vector space include all the conditions for being a subspace O D. True because the conditions for a subspace include all the axioms for being a vector space d. R is a subspace of R3. Is this statement true or false? O A. True because R's contains the zero vector, and is closed under vector addition and scalar multiplication O B. False because RS is not even a subset of R2 O C. False because R is not even a subset of R3 O D. True because R contains the zero vector, and is closed under vector addition and scalar multiplication e. A subset H of a vector space V is a subspace of V if the following conditions are satisfied: (i) the zero vector of V is in H, (ii) u, v, and u + v are in H, and (iii) c is a scalar and cu is in H. Is this statement true or false? O A. False; parts (ii) and (ili) should state that u and v represent all possible elements of H. O B. True; this is the definition of a subspace. O C. False; part (i) is not required. O D. False; these conditions are stated correctly, however there is at least one additional condition