I'm having some problems with the second part of this problem.

Let and let

So the first part says to Evaluate DF(a) and write it as DF(a)=[A|B] (a partitioned matrix) where A is a 3x2 matrix and B is a 3x3 matrix.

I got:

and

I need to show that if then the equation F=0 defines implicitly as a function of near a (that is the function f:R^2--->R^3, y=f(x)).