A matrix M R 2x2 is a linear transformation: R 2 R 2 . Given a dataset {(xi, yi)} i=1 N where x i , y i R 2 . We are going to fit a linear...

A matrix M ∈R2x2 is a linear transformation: R2 → R2. Given a dataset {(xi, yi)}i=1N where xi, yi ∈ R2. We are going to fit a linear transformation y = Mx.

(i) (2 pts) How many degrees of freedom does M have? How many samples are required to find M? 

(ii) (1 pt) Suppose we have a dataset {(xi, yi)}Ni=1 and want to fit y = Mx. Formulate the fitting problem into the form of a least squares problem:

argminm∥Am − b∥2 where m is some vector that has all the parameters of M.