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Each swimmer is allowed to compete in 7 events at a swim meet.
- Danny got first place 3 times, second place 1 time, third twice, and fourth once.
- John got first 2 times, second place 3 times, third twice, and didn’t place fourth.
- Kenny didn’t place first, but was second once, third four times, and fourth two times.
- Sean placed first once, second twice, third three times, and fourth once.
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 in second, 10 in third, and 5 in fourth.
- The Pirates swim team had 6 people get first place, 7 in second, 3 in third, and 1 in fourth.
- Devil Rays Aquatic Club had 9 people get first, 2 in second, 5 in third, and 7 in fourth.
- The Manta Rays swim team had 4 first-place winners, 3 second, 2 third, and 1 fourth.
Be prepared to discuss the following in your exploration meeting:
- Create a matrix for the individual swimmers and name it A. What are the dimensions?
- Create a matrix for the teams and name it B. What are the dimensions?
- Create a matrix for the points awarded and name it C. What are the dimensions?
- First place receives 6 points, second 4, third 3, and fourth 2.
- Which swimmer got the most points?
- Which team won the trophy?
- Explain how you got your answers.
- Does the order in which you multiply the matrices affect your results? Explain.
- For the first two meets of the season, Danny, John, Kenny, and Sean had the exact same results. Use scalar multiplication to determine the totals of first, second, third, and fourth place for each individual swimmer.
- Look back at what you did for questions 4 and 5. How does this relate to your understanding of vectors?
- The top three teams qualified to compete at the state competition. Use the following information to create a system of equations where x is the points for first place, y 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 a method of your choice (Cramer’s rule or the inverse method) to get the answers. Explain why you chose that particular method.