Let {x1, x2... xn} be a spanning set for V.

If we add an additional vector xn+1 to the set , will we still have a spanning set?

I'm struggling to understand linear span. I know that if x1, x2.. xn is a spanning set for V, then it takes all the linear combinations of c1x1, c2x2.. cnxn.

I don't see how this extra vector affects it though?