Question about linear regression

Let K : {1,2, 3} be a categorical variable with three levels, and consider tting the model E(Y|K) = 50 + 13le + 52KB: where K;- : 1 if K = 3'. Assume each group has the same sample size me, and 3m, : n. a) Show that 58(5llK) : 36(32|K). b) Show that 38(50|K) : 36(30 + BK) : 380% + 32|K). (You only need to carry out these derivations to the point that you can show the equality, not derive the nal values. Hint: You'll need to start taking a matrix inverse, but you may not need to complete the inverse. There is a closed form solution for a 333 matrix inverse.)