1. If given A(x,y)=(1/x, 1/y^2) and m=(1,1), how do I show that Df (m)(x,y)=(-x, -2y)?

2. If T: Rn -> Rm is a linear transformation where T(x)=Mx for a m x n matrix M. How do I show that for every a ∈ Rn, DT(a)=M?