Why span(k) Contains More Than k

[nhrock3]

k is a group of vectors

W is a subspace.

why if W $$\subseteq$$k then W $$\subseteq$$span(k)

??

span(k) is wider then k



it contains all the combinations of k

 

[Undoubtedly0]

You're logic seems fine. Certainly if W is a subset of k, then W is a subset of something 'wider' than k (span{k}).

 

[Mark44]

There's something that bothers me about this. If W is a subspace, and W is also a subset of a set of vectors, then it seems to me that W must be the zero vector in whatever space we happen to be working with.

Any other subspaces consist of an infinite number of vectors, so couldn't be a subset of a finite collection of vectors.

If W = 0, then clearly W is a particular linear combination of the vectors in set k, so is in span(k).