I need help with this linear algebra

Example 3.3. Suppose I have 5' teams, A, B, and C. Suppose Team A heat Them B by '9', Team C beat Team A by 1, Team C heat team B by I, and Team 3 beat Team 0' by 10, we would get the following system of equatomr.' EVArig}: 7 rcrA=l rgr3=1 TIETC: 10 Which will give us the follml'ing matrix system, Xr = b: 1 1 o T 7 1 o 1 A _ 1 0 1 1 ' T9 _ 1 (8) 011") 10 Note that each row of our system of equations representing a partimilar game from the data set. Our columns represent the different teams being ranked. This usually means in practice that our system has more rows than columns. 11. We have a problem This system is inconsistent. That is, there are solutions. What method can we use to \"approximate\" a solution? 12. Use least squares to solve the following inconsistent solution. 1 1 o T 1 0 1 _ 1 0 1 1 r' 1 0 1 1 1o 30 13. We now have a new problem: This system has innitely many solutions. To x this, we replace the last l'UW of our new matrix with all 1's and the last entry in the vector with G. We won't go into the technical details for why we do this, but this adjustment forces the ratings to sum to 0. Do this and solve the new system. 14. The Colley and Massey Rating Methods are good, but what are some other things we may want to consider when making our ranking