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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

Properties of Determinants

Gilbert StrangDistinguishedMIT

Professor

49:12·2009·undergraduate level

This lecture systematically covers the axiomatic properties of determinants, including their behavior under row operations, transposition, and scalar multiplication.

MathematicsLinear AlgebraDeterminantsMatrix PropertiesRow Operations

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

LecturerAll lecturers →
Gilbert StrangDistinguished

MIT Professor Emeritus & Author of Introduction to Linear Algebra

MIT Professor of Mathematics Emeritus whose legendary 18.06 Linear Algebra and 18.085 Computational Science courses educated millions of engineers and mathematicians.

3 courses · 56 lecturesCanon
Previous · Lecture 16

Orthogonal Matrices and Gram-Schmidt

Next · Lecture 18

Determinant Formulas and Cofactors

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