Explore the concept of controllability in linear systems through this 33-minute lecture. Begin with simple tests using the rank of the controllability matrix on intuitive examples. Delve into Chapter 8 of "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz. Access additional chapters at http://databookuw.com/databook.pdf. Gain valuable insights into when a linear system can be controlled, enhancing your understanding of control theory and its applications in engineering and science.