Explore a gentle introduction to modeling complex time-varying systems using matrices and vectors through a probabilistic weather model. Learn how to represent weather states as vectors and update probabilities using matrix multiplication. Follow along with code examples in both Python and MATLAB as you build a simple yet insightful model for predicting weather patterns. Discover how to store and manipulate weather state probabilities, implement dynamical system update rules, and gain insights into making the model more realistic. This educational video provides a practical foundation for understanding matrix-based modeling techniques applicable to various fields beyond meteorology.