In the generalized regression model, if theKcolumns of X are characteristic vectors of , then ordinary least

In the generalized regression model, if theKcolumns of X are characteristic vectors of Ω, then ordinary least squares and generalized least squares are identical. (The result is actually a bit broader; X may be any linear combination of exactly K characteristic vectors. This result is Kruskal’s theorem.)
a. Prove the result directly using matrix algebra.
b. Prove that if X contains a constant term and if the remaining columns are in deviation form (so that the column sum is zero), then the model of Exercise 8 is one of these cases. (The seemingly unrelated regressions model with identical regressor matrices, discussed in Chapter 10, is another.)