1. Sports leagues such as the NBA, NFL, and NHL rank teams throughout the season. Rankings take in multiple variables, such as who won, who played each other, how much teams won by, and so on. Linear algebra can be used to produce accurate rankings of teams in a league. To build our understanding of how these systems work, we will focus our study on a one-on-one basketball league. Vanessa, Paul, and LeBron James are in the league. Vanessa destroyed Paul 33-10, LeBron and Paul tie 20-20, and LeBron beats Vanessa 30-5. (a) Construct a 3 x 3 matrix A that encapsulates these scores, where Vanessa's scores are in the first row, Paul's in the second, and LeBron's in the third. What do the entires in the columns represent? Summarize in a sentence or two. (b) The ranks of the players are dependent on the ranks of the other players. To do this, we can define a "ranking vector" 7 rp where TL TV = a(33rp + 5rL) rp = a(10ry + 20rL) %3D TL = a(30ry + 20rp) Here, a is a proportionality constant. Write the above as a matrix-vector equation. (c) What is special about the vector F relative to the matrix vector equation in the previous part? Sum- marize in a sentence or two.

1. Sports leagues such as the NBA, NFL, and NHL rank teams throughout the season. Rankings take in multiple variables, such as who won, who played each other, how much teams won by, and so on. Linear algebra can be used to produce accurate rankings of teams in a league. To build our understanding of how these systems work, we will focus our study on a one-on-one basketball league. Vanessa, Paul, and LeBron James are in the league. Vanessa destroyed Paul 33-10, LeBron and Paul tie 20-20, and LeBron beats Vanessa 30-5. (a) Construct a 3 x 3 matrix A that encapsulates these scores, where Vanessa's scores are in the first row, Paul's in the second, and LeBron's in the third. What do the entires in the columns represent? Summarize in a sentence or two. (b) The ranks of the players are dependent on the ranks of the other players. To do this, we can define a "ranking vector" 7 rp where TL TV = a(33rp + 5rL) rp = a(10ry + 20rL) %3D TL = a(30ry + 20rp) Here, a is a proportionality constant. Write the above as a matrix-vector equation. (c) What is special about the vector F relative to the matrix vector equation in the previous part? Sum- marize in a sentence or two.

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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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

Please help me solve this problem I need the Solution ASAP
By following Bartleby rules...Please only solve the first 3 subparts(a,b,c)

Thanks

1. Sports leagues such as the NBA, NFL, and NHL rank teams throughout the season. Rankings take in
multiple variables, such as who won, who played each other, how much teams won by, and so on. Linear
algebra can be used to produce accurate rankings of teams in a league.
To build our understanding of how these systems work, we will focus our study on a one-on-one basketball
league. Vanessa, Paul, and LeBron James are in the league. Vanessa destroyed Paul 33-10, LeBron and
Paul tie 20-20, and LeBron beats Vanessa 30-5.
(a) Construct a 3 x 3 matrix A that encapsulates these scores, where Vanessa's scores are in the first
row, Paul's in the second, and LeBron's in the third. What do the entires in the columns represent?
Summarize in a sentence or two.
(b) The ranks of the players are dependent on the ranks of the other players. To do this, we can define
a "ranking vector" =
where
TL
ry = a(33rp + 5rL)
rp = a(10ry + 20r1)
TL = a(30ry + 20rp)
Here, a is a proportionality constant. Write the above as a matrix-vector equation.
(c) What is special about the vector F relative to the matrix vector equation in the previous part? Sum-
marize in a sentence or two.
(d) Using your understanding of linear algebra thus far, as well as a calculator, the value of a.
(e) Now that you have a, write r in a parametric vector form. What is the overall ranking in the league?
For more information on how to use linear algebra to do team rankings, take a gander at the article: "A
Matrir Based Ranking Method with Application to Tennis" by Geir Dahl. It is a much more complex
example.

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