Partition matrices: Consider using a partition matrix in OLS. That is, consider X = [X1,X2] and = 1 2 where X1 is n × r1, X1 is n × r2, 1 is r1 × 1, 2 is r2 × 1, and r1 + r2 = r, the overall number of columns in X. When we take the inverse of a 2 × 2 partition matrix A B C D −1 = (A − BC−1D)−1 −(A − BD−1C)−1BD−1 −(D − CA−1B)−1CA−1 (D − CA−1B)−1 Find the equations for ˆ 1 and ˆ 2 using the OLS estimator ˆ = (X0X)−1X0y