Vectors & Matrices

Tip-to-tail addition, scaling, subtraction, vectors inside figures, and the section formula.

u·v two ways, angles from the sign, perpendicularity tests, and the |u+v|² toolbox.

The third coordinate: 3D magnitudes and dot products, the box diagonal, and normal vectors of planes.

Grids with an address system: entrywise arithmetic, row-times-column multiplication, identity and powers.

ad − bc, the 2×2 inverse, Cramer's rule, and matrices as transformations — the capstone.

Reflections, rotations, enlargements and translations as matrices, then composing and naming them.

Augmented matrices and row operations, Gauss's method, 3×3 determinants and inverses, and Cramer's rule.