Let s<n and A an s x n matrix with entries in the field F. Show that there is a non-zero X in F^nx1 such that AX=0

I know that X is non-zero, since the columns outnumber the rows. I think I'm supposed to use a theorem to prove this, saying that for a vector space spaned by a finite set of vectors, any independent set of vectors is finite and contains no more than the number of elements in the set that spans.