The question:

Show that the set S = { } where A = is a subspace of Explain why each column of the matrix belongs to the set S.

I'm having trouble with this one. I recognize the Ax=b form, but I'm not sure how to prove that it is a subspace. I know the Subspace Theorem, and I managed to show that it isn't an empty-set by substitutingx=0into the matrix. But when it comes to closure under vector addition, I'm getting confused. Could someone shed some light on how I should attempt this? Thanks.