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MIT 18.06: Linear Algebra →0/20
1

The Geometry of Linear Equations

39:49
2

Elimination with Matrices

47:42
3

Matrix Multiplication and Inverse Matrices

46:30
4

Factorization into A = LU

48:05
5

Transposes, Permutations & Vector Spaces R^n

47:41
6

Column Space and Nullspace

46:01
7

Solving Ax = 0 — Pivot Variables, Free Variables & Rank

43:19
8

Solving Ax = b — Complete Solutions & Full Rank Cases

47:19
9

Independence, Basis, and Dimension

50:14
10

The Four Fundamental Subspaces

49:20
11

Matrix Spaces; Rank 1; Small World Graphs

45:56
12

Graphs, Networks, Incidence Matrices

47:57
13

Orthogonal Vectors and Subspaces

49:48
14

Projections onto Subspaces

48:51
15

Projection Matrices and Least Squares

48:05
16

Orthogonal Matrices and Gram-Schmidt

49:10
17

Properties of Determinants

49:12
18

Determinant Formulas and Cofactors

53:17
19

Cramer's Rule, Inverse Matrix, and Volume

51:01
20

Eigenvalues and Eigenvectors

51:23

Determinant Formulas and Cofactors

Gilbert StrangMIT

Professor

53:17·2009·undergraduate level

This session derives explicit formulas for determinants using permutations and introduces the cofactor expansion method for calculating determinants of arbitrary size matrices.

MathematicsLinear AlgebraDeterminant FormulasCofactor ExpansionPermutations

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

Previous · Lecture 17

Properties of Determinants

Next · Lecture 19

Cramer's Rule, Inverse Matrix, and Volume

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