This course teaches what vectors and matrices do (not just how to compute with them). You'll learn geometric intuition, algebraic techniques, and practical uses in physics and computer graphics. Designed for motivated high-school students, it balances conceptual lessons, worked examples, and short projects.

Start with vector basics and vector spaces, move to matrix arithmetic and transformations, then learn how different coordinate systems (bases) simplify problems. Each unit contains 5–7 step wise lessons with clear section titles: definitions, worked mechanics, geometric interpretation, short practice, and one application or mini-project. By the end students will solve linear systems, perform and combine geometric transforms, and change coordinates between bases.