Ken's Puzzle of the Week
Nine Digits in Sums

Is it possible to find 3-digit numbers A,C,D,F, such that:

• A+D=G, and C+F=I
• B is the average of A and C.  E is the average of D and F.  H is the average of G and I.
• All digits 1-9 are used once in each row and column.

I'll admit I'm not sure if the complete puzzle can be solved.  If not, can it be solved if the 9-digits restriction applies only to the first two rows and the outside columns?

Source: Original.