The Geometry of Linear Equations
39:49Elimination with Matrices
47:42Matrix Multiplication and Inverse Matrices
46:30Factorization into A = LU
48:05Transposes, Permutations & Vector Spaces R^n
47:41Column Space and Nullspace
46:01Solving Ax = 0 — Pivot Variables, Free Variables & Rank
43:19Solving Ax = b — Complete Solutions & Full Rank Cases
47:19Independence, Basis, and Dimension
50:14The Four Fundamental Subspaces
49:20Matrix Spaces; Rank 1; Small World Graphs
45:56Graphs, Networks, Incidence Matrices
47:57Orthogonal Vectors and Subspaces
49:48Projections onto Subspaces
48:51Projection Matrices and Least Squares
48:05Orthogonal Matrices and Gram-Schmidt
49:10Properties of Determinants
49:12Determinant Formulas and Cofactors
53:17Cramer's Rule, Inverse Matrix, and Volume
51:01Eigenvalues and Eigenvectors
51:23Cramer's Rule, Inverse Matrix, and Volume
This lecture presents Cramer's Rule for solving linear systems, connects the adjoint matrix to the inverse, and illustrates the geometric interpretation of determinants as volume.
MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
Determinant Formulas and Cofactors
Next · Lecture 20Eigenvalues and Eigenvectors