Determine whether each statement is True or False Justify ea

Determine whether each statement is True or False. Justify each answer. A vector is any element of a vector space. Is this statement true or false? A. False; not all vectors are elements of a vector space B. False; a vector space is any element of a vector. C. True by the definition of a vector space. 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? A. True because for each u in V, -u = (-1)u B. False because for each u in V, there is a vector -u in V such that u + (-u) = 0 C. True because for each u in V, there is a vector -u in V such that u + (-u) = 0 D. False because for each u in V, - u = u A vector space is also a subspace of itself. 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

Solution

1)C.

2)A.

3)D