(a) Let be a subset of a vector space . is a subspace of if and only if the following two conditions hold:
i) is closed under the sum operation. That is to say, whenever are elements of .
ii) is closed under the scalar multiplication. That is to say, whenever and
Step-by-step explanation:
For the part (b) we have the set of all sequences of the form, where . Observe the if you multiply any sequence of this form by and scalar then the sequence stops being like the given form. For example, let . Then:
This implies that the set under consideration is not closet under scalar multiplication, which implies that the set is not a subspace of the vector space of all sequences.
This is because he would find the most students in the cafeteria. It is not A because not everyone goes to basketball games. It's not C because you're looking for where you will find the most students. And it's not D because thats local and he is trying to find how many students want to organize a club NOT random people at a movie theater.