Hi,

I hope someone can help. I'm trying to understand the following theorem (about subspaces):

I understand the first property. However the second property doesn't make any sense to me. My professor said that the second property is saying that out of all the sets which have property (1), the span must be the smallest. I don't see how this is communicated in property (2). Could someone provide some clarification on this? If you could provide it in the context of a column space that would be the most helpful since this is a subspace that I am most familiar with.

- otownsend