(Algebra 2)

As you read through the following scenarios,
be prepared to create matrices and do any
operations on those matrices.
Each swimmer is allowed to compete in
seven events at a swim meet. Here are their
results from the first meet of the season.
•Danny got first place 3 times, second place 1
time, third place 2 times, and fourth place 1
time.
•John got first place 2 times, second place 3
times, third place 2 times, and he never
placed fourth.
•Kenny never placed first, but got second
place 1 time, third place 4 times, and fourth
place 2 times.
•Sean got first place 1 time, second place 2
times, third place 3 times, and fourth place 1
time.

The club teams are waiting to see which
trophy they will be getting. Their trophy is
based on the amount of points each team
received.

•The Eagles Aquatics team had 8 people get
first place, 9 people get second place, 10
people get third place, and 5 people get
fourth place.
•The Pirates swim team had 6 people get first
place, 7 people get second place, 3 people
get third place, and 1 person get fourth place.
•Devil Rays Aquatic Club had 9 people get
first place, 2 people get second place, 5
people get third place, and 7 people get
fourth place.
•The Manta Rays swim team had 4 people
get first place, 3 people get second place, 2
people get third place, and 1 person get
fourth place.
Swimmers who get first place receive 6
points, swimmers who get second place
receive 4 points, swimmers who get third
place receive 3 points, and swimmer who get
fourth place receive 2 points.

Questions:

1)Create a matrix for the individual swimmers
and name it A. What are the dimensions of
matrix A? Enter your matrix as part of your
answer.

2) Create a matrix for the teams and name it
B. What are the dimensions of matrix B?
Enter your matrix as part of your answer.

3) Create a matrix for the points awarded to
someone who wins first place, someone who
wins second place, someone who wins third
place, and someone who wins fourth place.
Name the matrix C. What are the
dimensions of matrix C? Enter your matrix as
part of your answer.

4) If first place receives 6 points, second
place receives 4 points, third place receives
3 points, and fourth place receives 2 points,
which swimmer got the most points?

5) If first place receives 6 points, second
place receives 4 points, third place receives
3 points, and fourth place receives 2 points,
which team won the trophy?

6) Does the order in which you multiply the
matrices affect your results? Explain.

7) At this point in the season, there have now been two swim meets. Danny, John, Kenny,
and Sean each had the same results in the
second meet as they did in the first meet,
represented by matrix A from the first question.

8) Using the matrix that you found in the
previous question, explain what the second
column of the matrix represents and what
each value in that column represents.


9) The top three teams qualified to compete
at the state competition. At the state
competition, however, scoring is done
differently than at the other meets. Use the
following information to create a system of
equations where I is the points for first place,
g is the points for second place, and z is the
points for third place.
Results:
*Eagles got 5 first-place, 3 second-place, and
4 third-place finishes with a team total of 67
points.
•Pirates got 2 first-place, 5 second-place, and
5 third-place finishes with a team total of 56.
• Devil Rays got 6 first-place, 3 second-place
and 3 third-place finishes with a team total of
72.

We can't believe the Devil Rays came from
behind and won! We need to determine how
many points were awarded for each place.
Use Cramer's rule or inverse method to get
the answers. Explain your process.