This is a course on understanding, manipulating, and applying linear systems of equations and, more broadly, linear relationships between variables. The ideas and tools you will learn are immensely useful in a wide variety of application domains, including physics, engineering, big data, data visualization, and more. You will become familiar with vectors and matrices, linear systems of equations, vector spaces, inner products, eigenvectors and eigenvalues and the more general singular values. You will also learn to interpret matrices as linear transformations and to understand the geometrical interpretation for operations such as solving linear systems of equations and least-squares fitting of data to models. Throughout the course, the tools will be related to specific applications to show how linear algebra is used to solve real-world problems. Examples include Google's PageRank algorithm, cryptography, coding theory, genetics, bioinformatics, image compression, linear programming (optimization), networks, and Markov chains. Cannot be taken for credit in addition to CAS MA 142 or CAS MA 242.