matrices creating matrices and solving them

Each swimmer is allowed to compete in 7 events at a swim meet. Danny got first place 3 times, second place 1 time, third 2 times, 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. 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, 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. 

1. First place receives 6 points, second 4, third 3, and fourth 2. Which swimmer got the most points? Which team won the trophy? Show how you found that out.
2. Does it matter in what order you multiply the matrices? Explain.
3. If you were to find out the total number of points scored by individuals and teams, how would you go about doing that?
4. Look back at what you did for questions 1 and 2. How does this relate to your understanding of vectors?
5. Come prepared to share another example of a problem in the real world that can be solved using matrices.


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