C. I. NKEKI

This project work provides an overview on the application of linear algebra to artificial intelligence including natural language processing and machine learning. We discuss how linear algebra operations such as matrices, linear transformations, eigen values and eigen vectors, are used to optimize AI models, analyze complex data structures and enable efficient computation. Beginning with an overview of fundamental concepts in linear algebra, such as vectors, matrices, and linear transformations, the study delves into specific applications of these concepts in AI. One key area of focus is machine learning, where linear algebra forms the backbone of algorithms for tasks such as regression analysis, and principal component analysis for dimensionality reduction. This work also showcases the versatility of linear algebra by delving deep into the various reaches of linear algebra into many other fields and areas of study such as economics, physics and engineering.

This study applies the transportation model as an optimization tool to address tanker routes problem in petroleum distribution. The research focuses on minimizing transportation cost reducing fuel consumption, and improving operational efficiency in the delivery of petroleum products from supply depots to various demand centers using linear programming techniques, the transportation problem was formulated to determine the optimal routes and cost- effective allocation of tankers. Data were obtained for selected depots and filling stations in Benin city Edo state and analyzed using the Northwest Corner Rule (NCR), Least Cost Method (LCM), Vogel Approximation Method (VAM), Russell Approximation Method (RAM) and Stepping-Stone Optimal Solution