9 In the Bloomington Girls Club basketball league, the following games have been played: team A beat team B by 7 points, team C beat team A by 8 points, team B beat team C by 6 points, and team B beat team C by 9 points. Let A, B, and C represent “ratings” for each team in the sense that if, say, team A plays team B, then we predict that team A will defeat team B by A  B points. Determine values of A, B, and C that best fit (in the least squares sense) these results. To obtain a unique set of ratings, it may be helpful to add the constraint A B C  0. This ensures that an

“average” team will have a rating of 0.