Explore how vectors and matrices help describe mathematical relationships and solve problems in linear algebra. Drawing on content from Jeffrey Holt, author of Linear Algebra with Applications, published by Macmillan Learning, this course introduces foundational vector concepts and matrix methods.

You will begin with vectors in Euclidean space and examine how combinations of vectors form a span. You will also study linear independence, learning to determine whether a set of vectors contains redundant relationships. From there, you will explore linear transformations and matrix algebra, including matrix inverses and LU factorization. You will apply matrix methods to Markov chains, connecting these techniques to models that describe transitions between states. Through readings, practice exercises, and homework, you will strengthen your ability to work with vectors and use key matrix methods. The course includes approximately 12 hours of learning material. This course is part of the Foundations of Linear Algebra Specialization and can also be taken independently.