LA41 Determinants: Definition via Elementary Products

Definition of Determinants via Signed Elementary Products. Subscribe ‪@Shahriari‬ for more undergraduate math videos. Inversions, Even & Odd Permutations, and Signed Elementary Products are defined in order to define the determinant of an nxn matrix. It is shown that the determinant of an upper triangular matrix is the product of the diagonals, and the determinant of a matrix with a row of zeros is zero.
00:00 Introduction
00:14 Context/Plan
01:17 Definition: Permutations
01:41 Example: Permutations
01:52 The number of permutations of n objects is n!
02:18 Definition: Inversions
03:05 Definition: Odd & Even Permutations
03:31 Alternate Definition of Odd & Even Permutations from Group Theory
04:34 Definition: Elementary Products
05:44 Example: Elementary Products
06:31 The permutation corresponding to an Elementary Product
07:30 Signed Elementary Products
08:18 Definition of Determinant
09:25 Determinant of 2x2 matrices
10:05 Determinant of 3x3 matrices
11:05 Determinant of upper triangular matrices
12:36 Determinant of a matrix with a row of zeros
13:14 List of Videos on Determinants

This is a video in a series of lectures on linear algebra. The series is a rigorous treatment meant for students with no prior exposure to linear algebra. In this full undergraduate course in linear algebra, general vector spaces and linear transformations are emphasized.
This is also a part of a series of lectures on Determinants of Matrices.
LA41 Definition of Determinant    • LA41 Determinants: Definition via Ele...  
LA42 Determinant is Multi-linear and Alternating    • LA42 Determinant is Multi-linear and ...  
LA43 Determinants & Elementary Row Operations    • LA43 Determinants & Elementary Row Op...  
LA44 A invertible iff Det(A) nonzero; Det(AB) = Det(A)Det(B)    • LA44 A invertible iff Det(A) not zero...  
LA45 Cofactor Expansion for Determinants

For an annotated list of available Linear Algebra videos see
https://pomona.box.com/s/oahafa797tj5...
Linear Algebra YouTube Playlist:   • Linear Algebra, a Retro introduction  

Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA USA
Shahriari is a 2015 winner of the Mathematical Association of America's Haimo Award for Distinguished Teaching of Mathematics, and five time winner of Pomona College's Wig teaching award.