Show the steps, please

3. In this exercise, we will see how to use projections to solve problems with affine constraints. The problem is broken down into five steps that are each as simple as possible. Our target is solving the problem min || A3 b|| 2 where we require 19x = 0, that is, we require that the solution is perpendicular to the vector of all ones. (a) Write down the projector Ponto the subspace perpendicular to the span of the vector of all ones. (b) Make the variable substitution = Pz where z is allowed to be free. Explain why representing a this way will get us the solution that we need. (c) Write down the modified least squares problem with respect to z that we get after plugging in I = Pz into the original least squares problem. (a) Write down the linear system that we need to solve to get the solution 2, and explain why we can always solve that system. (e) Explain how you get the final x that solves the problem once you have the solution z