# An Application of Matrices to the Spread of the COVID 19

5-2022

Thesis

## Degree Name

Master of Science (MS)

## Department

Mathematics

Dr. Jasang Yoon

Dr. Paul Bracken

Dr. William Heller

## Abstract

We represented a restaurant seating arrangement using matrices by using 0 entry for someone without covid and 1 entry for someone with covid. Using the matrices we found the best seating arrangements to lessen the spread of covid. We also investigated if there was a factor needed to create a formula that could calculate the matrix that shows who would be affected with covid with each seating arrangement. However, there did not seem to be a clear pattern within the factors. Aside from covid applications, we also investigated the symmetries in seating arrangements and the possible combinations with these arrangements taking into consideration the equivalent matrices. We realized that the most equivalent matrices possible was 8, which happened when there were no symmetries in the matrices. There were 4 equivalent matrices when there was diagonal, vertical, or rotational symmetry. There were 2 equivalent matrices when there was diagonal and rotational or vertical and rotational symmetry. There was only 1 equivalent matrix where there was all symmetries present. This knowledge was used to create a new method for the 4 by 4 case in order to find all possible combinations of seating arrangements and this new method made the process much more efficient. After concluding our results using this method, we realized there was symmetry for possible combinations and for ways of spreading covid which can be seen in the list of tables.