Each swimmer is allowed to compete in seven events at a swim meet.

Question

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.

Create a matrix for the individual swimmers and name it A. What are the dimensions of matrix A?

Create a matrix for the teams and name it B. What are the dimensions of matrix B?

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?

First place receives 6 points, second 4, third 3, and fourth 2. Which swimmer got the most points?

Which team won the trophy?

Answer 1

Starting out, it is best to label your rows and columns so that your matrices make sense in the context of the problem:

1st place 2nd place 3rd place 4th place

Danny [ 3 1 2 1 ]

John [ # # # # ]

Kenny [ # # # # ]

Sean [ # # # # ]

Hence:

[ 3 1 2 1 ]

[ # # # # ]

A = [ # # # # ]

[ # # # # ]

Similarly, matrix B is constructed with rows representing teams and columns representing number of specific place finishes.

For matrix C, consider how it might be used with matrix multiplication on matrix B. This will help you determine that the row/column values represent.