Problem set 2 Bean 6340 Linear algebra 1. Partition matrices: Consider using a partition matrix in OLS. That is, consider X = [X11 X2] and _ #31 '3 ' [a where X1 is n x 1'1, X1 is n X 1'2, ,81 is 1'1 x l, 52 is r2 X l, and 7'1 + r2 = 1', the overall number of columns in X. When we take the inverse of a 2 X 2 partition matrix [A Ell =l (\"9'19\" _ *'HD'Ie-IFD'Il C D 7(DeCA 113) 10A 1 (DeCA 113) 1 Find the equations for ,31 and 32 using the OLS estimator E = (X'X)'1X'y Programming 2. White estimator: Extend the linear model code we wrote in class to implement a White corrected OLS estimator. The robust variance covariance matrix for the White estimator is Var} \"a = (x'xrlx'mx'xrl where Q = diag(2). You can either create a new inheriting class or you can add the functionality as an option in the least squares code that we wrote