12. (5%) Let S be the set of all positive real numbers. Now, we want to make S as a
vector space in V by asking the following definitions for vectors, vector addition,
and scalar multiplication:
ㆍ Each element of S will be considered as a "vector" in V.
ㆍ For A, B
S, a "vector sum" is defined as
A+ B ≡ AB
where the product on the right is the usual product of two real numbers.
ㆍFor
R (real number), and A
S, a "scalar multiplication" is defined as
cㆍA≡ Ac,
that is the real number A raised to the c power.
Based on these, what is the zero vector in V?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
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