I forgot to ask one more question that I had on mind,

If u belongs to Span(A) does it mean that u is equal to v_{i}when 1<i<k (including 1 and k) that Span(v_{1},v_{2},.....,v_{i},...v_{n})

or does it mean that with the linear combinations of vectors of A I can get the vector u?

In other words doest it mean u belongs to the set A or you can get u by the linear combinations of the vectors that belong to A