Lecture 1: The Geometry of Linear Equations (18.06)

Elimination with Matrices

Matrix Multiplication and Inverse Matrices

MIT 18.06 Lecture 4: Factorization into A = LU

MIT 18.06 Lecture 5: Transposes, Permutations & Vector Spaces R^n

MIT 18.06 Lecture 6: Column Space and Nullspace

MIT 18.06 Lecture 7: Solving Ax = 0 — Pivot Variables, Free Variables & Rank

MIT 18.06 Lecture 8: Solving Ax = b — Complete Solutions & Full Rank Cases

Lecture 9: Independence, Basis, and Dimension (18.06)

Lecture 10: The Four Fundamental Subspaces (18.06)

Lecture 11: Matrix Spaces; Rank 1; Small World Graphs (18.06)

Lecture 12: Graphs, Networks, Incidence Matrices (18.06)

Lecture 14: Orthogonal Vectors and Subspaces (18.06)

Lecture 15: Projections onto Subspaces (18.06)

Lecture 16: Projection Matrices and Least Squares (18.06)

Lecture 17: Orthogonal Matrices and Gram-Schmidt (18.06)

Lecture 18: Properties of Determinants (18.06)

Lecture 19: Determinant Formulas and Cofactors (18.06)

Lecture 20: Cramer's Rule, Inverse Matrix, and Volume (18.06)

The Geometry of Linear Equations