how do u prove these claims?

http://www.mathhelpforum.com/math-he...1&d=1234126619


i think the first part, we can say that assume A represents a linear map and dimV is greater than dimW. So alpha is surjective which means n(A) is nonzero.

And k is the least number makes the linear map surjective, which means, dimV=dimW+1, and n(A)=1

but i got no idea with (b) and etc.