Explore fundamental concepts of linear algebra in this comprehensive lecture from the "Great Theoretical Ideas in Computer Science" series. Delve into linear combinations of vectors, discover fascinating applications with Fibonacci sequences, and gain insights into vector spaces and subspaces. Investigate linear independence, examine a nontrivial linear algebra theorem, and learn about sending messages on noisy channels. Master essential mathematical principles that form the backbone of computer science and enhance your problem-solving skills in this engaging 74-minute presentation.