Question

Give an example show the difference between a subset and a subspace.
I don't know, please help

Answer 1

A subset of L={a,b,c} is {a,b}, where a,b and c is any type of element. That is, a subset consists of the entire set (L), some elements of the set or the empty set.

A subspace must include the zero vector. So, if a,b,c are vectors, at least one of them must be the zero vector if S = {a,b,c} is to be a subspace. A subset of a,b,c will also be a subspace if one of the elements in this subset includes the zero vector.

So, subsets are general groupings of elements, while a subspace has the additional property that it includes the zero vector. Also, a subspace includes all linear combinations of the elements of it's members, a subset of elements does not necessarily have this property, which can be quite arbitrary, such as apples, oranges or cars.

Answer 2

hey, I 'm jealous, how can you remember everything like that? hehehe. anyway, thanks a lot.

Answer 3

You do see it though, right?

Answer 4

just after reading your comment

Answer 5

nice :)