Determine whether each statement is True or False Justify ea

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? A. O B. True by the definition of a vector space False: a vector space is any element of a vector. C. False: not all vectors are elements 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. s 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)o OB. True because for each u in V -u 1)u OC. True because for each u in V, there is a vector-uin v such that u + (-u)=0 O D. False because for each u in V,-u u G.A vector space is also a subspace of itself Click to select your answer

Solution

a) true yes

a vector space consists of all vectors.

every element of it is vector space

the reason is statement A

B) it is true

u + (-1).u = 0

u and -u are opposite of each other

the reason is statement B

C) yes vector space is a subspace of itself

all the axioms of subset is satisfied

the reason is statement A

D) it is true

and the reason is statement D

E) yes it is the definition