Problem set 2 Buan 6340 Linear algebra 1. Partition matrices: Consider using a partition matrix in OLS. That is, consider X = [X1, X2] and B = BI B2 where X1 is n x r1, X1 is n x 12, B1 is r1 X 1, B2 is r2 x 1, and r1 + 12 = r, the overall number of columns in X. When we take the inverse of a 2 x 2 partition matrix B (A - BD-'C)-1 D -(D - CA-1B)-1CA-1 -(A - BD-1C)-1BD-1 (D - CA-1B)-1 Find the equations for 1 and 32 using the OLS estimator B = (X'X)-1X'y