This project compares traffic flow before and after the installation of the new light rail in Lynnwood, Washington. Using linear algebra and systems of equations, we modeled how traffic moves through intersections near the station area and compared traffic count data from 2022 and 2025. Our hypothesis was that traffic would decrease after the installation of the light rail. However, after comparing the data, most traffic patterns stayed relatively similar, with only moderate changes in certain locations. This project also demonstrates how linear algebra can be applied to real-world systems such as transportation networks. 

With Seattle’s growing population putting more cars on the road, increasing traffic volumes have strained intersections, causing heavy congestion and making them unsafe for pedestrians and cyclists. To manage these commuter demands, this area is replacing high volume four-way stops with modern roundabouts. This project applies linear algebra to analyze traffic data and model network flow for a newly constructed roundabout in the Seattle Metro Area. Prior to construction, the intersection was a highly congested four-way stop experiencing heavy daily traffic. The roundabout was implemented to resolve these issues—improving road design to support pedestrian and bicycle access while simultaneously clearing vehicle congestion.

This project explores how linear algebra can be used to understand and classify image data. Many modern technologies, such as image search, facial filters, medical imaging, and security systems, rely on converting images into numerical data that computers can analyze. In this project, face images were represented as vectors and organized into a matrix. The main goal was to test whether Principal Component Analysis (PCA) could reduce high-dimensional face image data while still keeping enough information for classification. A self-collected dataset was used with three categories: normal, smiling, and with glasses. The hypothesis was that PCA would capture the most important image patterns and help classify similar images correctly. This project shows how linear algebra concepts, including matrices, vectors, eigenvalues, eigenvectors, and dimensionality reduction, can be applied to real image data. New “mystery images” were also tested to see whether the model could generalize to unseen photos. The results suggest that PCA is useful for reducing image data, but a larger and more varied dataset is needed for stronger real-world performance.

The project's purpose was to see what conclusions could be created by applying linear algebra to multiple regression models. Regression models are a form of linear equations, often used in statistics to define outputs based on varying characteristic inputs. To create the regression models, all previously sold properties within Seattle, Los Angeles, Dallas, and Boston were placed in a database corresponding to the city. For each individual property, its square footage, age, distance from central business district (CBD), and property type were used as relational variables, and totaled to the sold price. The top 10% of properties within each data set and any sales unfit of current market estimates were excluded from the list. The remaining entries were analyzed by Excel’s built-in regression analyzer to create a linear model composed of an intercept, four coefficient factors, and the estimated property price based on property characteristics. A Matrix is formed by using each characteristic coefficient as columns and the different cities as rows. Reducing this 4x4 matrix reveals every column to be a pivot column. This confirms the rank of A to equal 4, and also being a full-rank matrix. Through containing no non-pivot columns, the matrix A displays a relation of linear independence of the characteristic coefficient vectors. Through linear independence, there exists only one solution of characteristic coefficient values for any output vector. Linear independence also shows that no city’s regression coefficients can be made up of a linear combination of the other coefficients. Interpreting this reveals each regression model to have a differ direction and/or magnitude for each characteristic coefficient.