I just want to confirm that I'm on the right track.

I need to derive an expression for b^Y1.2 that refers solely to variances and covariances (that is, only to bi-variate and mono-variate terms).

I have come up with the following:

b-hatY1.2 = (CovY1)/(Var1) - (Cov1,2/V1)*(b-hatY2.1)

That should be correct, but I just wanted some feedback. Thanks!!