Determine whether each statement is True or False. Justify each answer. Is this

Question

Determine whether each statement is True or False. Justify each answer. Is this statement true or false? A. False because the conditions for a subspace do not include all the axioms for being a vector space. B. True because the axioms for a vector space include all the conditions for being a subspace. C. False because the axioms for a vector space do not include all the conditions for being a subspace D. True because the conditions for a subspace include all the axioms for being a vector space d. R^2 is a subspace of R^3. Is this statement true or false? A. True because R^2 contains the zero vector, and is closed under vector addition and scalar multiplication B. True because R^3 contains the zero vector, and is closed under vector addition and scalar multiplication c. False because R^3 is not even a subset of R^2 D. False because R^2 is not even a subset of R^3 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 and (iii) c is a scalar and cu is In H. Is this statement true or false? A. False; parts (ii) and (iii) should state that u and v represent all possible elements of H. B. False; part (i) is not required. C. True; this is the definition of a subspace D. False; these conditions are stated correctly, however there is at least one additional condition.

Explanation / Answer

1)D

2)C

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