Vectors & Matrices Arrows made of numbers, then grids that move them. Vectors in the plane and in space — components, dot products, geometry — followed by matrices, determinants, and inverses, ending where transformations begin. Taught from zero, no prior experience assumed.
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The course — 6 units, in order
01 Vectors & Coordinates What a vector is, components and magnitude, equal/opposite/parallel vectors, and unit vectors. Start 02 Vector Arithmetic Tip-to-tail addition, scaling, subtraction, vectors inside figures, and the section formula. Start 03 The Dot Product u·v two ways, angles from the sign, perpendicularity tests, and the |u+v|² toolbox. Start 04 Vectors in Space The third coordinate: 3D magnitudes and dot products, the box diagonal, and normal vectors of planes. Start 05 Matrices & Operations Grids with an address system: entrywise arithmetic, row-times-column multiplication, identity and powers. Start 06 Determinants, Inverses & Systems ad − bc, the 2×2 inverse, Cramer's rule, and matrices as transformations — the capstone. Start 07 Transformation Matrices Every geometric transformation as four numbers: reflections, rotations, enlargements, the translation that needs a third coordinate, and how to compose and name them. Start 08 Systems in Three Unknowns Elimination with the letters removed: augmented matrices, Gauss's method, the 3×3 determinant and inverse, and Cramer's rule. Start