You need to show that two sets are equal. Do this by showing that each set contains the other. If x_{0}and x_{1}are two solutions of Ax = b, then what do you get by subtracting these equations, i.e., what can be said about x_{0}- x_{1}?

If dim(Null(A)) = 0, then show (by contradiction) that A maps a basis into a basis. Therefore, b is a linear combination of the images of basis vectors under A. This gives at least one solution. Point i) implies that it is the only one.

P.S. Don't make your posts in huge bold font. If you have less than perfect vision (as I do), then feel free to increase the font while you are editing and previewing the post, then remove the [SIZE=...]...[/SIZE] tags before submitting.