Need help with Linear Algebra,the image is a similar example for it.Now use the Massey Method with a 10 max point differential for the following system:During the Early Part of the Season: Team B beats C by 8 points. Team D beats E by 5 points.During the Middle Part of the Season: Team A beats D by 10 points. Team E beats C by 5 points.During the Later Part of the Season: Team A beats E by 4. Team E beats B by 20 points.a. Draw a directed graph of this season.b. Write the system of equations for this season using the Massey method.c. Solve the system (using least squares) to find the ratings for each team, and use those ratings to rank them. 3.2.3 A Way to Use Scores - The Massey System of RankingSuppose we want to use a system of rating that incorporates the scores of the games. Onthe other hand, Kenneth Massey's method of sports rating creates a system of equationswhich is based on the score of the games played. Massey originally created this method forranking college football teams. Using the Massey Method, for each game, the difference inthe ratings correlates to the point differential. This is represented as a system: r₁ rj = bkwhere r, is the rating for team i and r, is the rating for team j and bk is the score differentialfor game k.Example 3.3. Suppose I have 3 teams, A, B, and C. Suppose Team A beat Team B by 7,Team C beat Team A by 1, Team C beat team B by 1, and Team B beat Team C by 10, wewould get the following system of equations:ΤΑTB = 7TC-TA = 1rc - TB: = 1TBTC = 10Which will give us the following matrix system, Xr = b:-10TADETBra0 110Note that each row of our system of equations representing a particular game from the dataset. Our columns represent the different teams being ranked. This usually means in practicethat our system has more rows than columns.

Given:During the Early Part of the Season, Team beats Team C by points and Team beats Team E by…

Answered: Now use the Massey Method with a 10 max…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Need help with Linear Algebra,the image is a similar example for it.

Now use the Massey Method with a 10 max point differential for the following system:
During the Early Part of the Season: Team B beats C by 8 points. Team D beats E by 5 points.
During the Middle Part of the Season: Team A beats D by 10 points. Team E beats C by 5 points.
During the Later Part of the Season: Team A beats E by 4. Team E beats B by 20 points.

a. Draw a directed graph of this season.

b. Write the system of equations for this season using the Massey method.

c. Solve the system (using least squares) to find the ratings for each team, and use those ratings to rank them.

3.2.3 A Way to Use Scores - The Massey System of Ranking
Suppose we want to use a system of rating that incorporates the scores of the games. On
the other hand, Kenneth Massey's method of sports rating creates a system of equations
which is based on the score of the games played. Massey originally created this method for
ranking college football teams. Using the Massey Method, for each game, the difference in
the ratings correlates to the point differential. This is represented as a system: r₁ rj = bk
where r, is the rating for team i and r, is the rating for team j and bk is the score differential
for game k.
Example 3.3. Suppose I have 3 teams, A, B, and C. Suppose Team A beat Team B by 7,
Team C beat Team A by 1, Team C beat team B by 1, and Team B beat Team C by 10, we
would get the following system of equations:
ΤΑ
TB = 7
TC-TA = 1
rc - TB: = 1
TBTC = 10
Which will give us the following matrix system, Xr = b:
-1
0
TA
DE
TB
ra
0 1
10
Note that each row of our system of equations representing a particular 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.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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