Скачать или смотреть LA44 A invertible iff Det(A) not zero; Det(AB) = Det(A) Det(B)

We prove (1) a matrix is invertible if and only if its #determinant is not zero; (2) Det(AB) = Det(A)Det(B) for square matrices A & B; (3) Det(A^{-1}) = 1/Det(A).#linearalgebra #matrices #determinants Subscribe ‪@Shahriari‬ for math videos for college.

00:00 Introduction & Lecture Plan
00:52 Definition of Determinant (   • LA41 Determinants: Definition via Elementa...  )
01:56 Elementary row operations (   • LA17 Elementary Row Operations, Reduced Ro...  )
02:36 Elementary row operations & Determinants (   • LA43 Determinants & Elementary Row Operations  )
03:03 Theorem & Proof: A invertible if and only if Det(A) is not zero
04:57 Elementary Matrices (   • LA31 Elementary Matrices and their inverses  )
06:20 Determinant of Elementary Matrices
07:07 Lemma & Proof: Det(EA) = Det(E)Det(A) if E is an elementary matrix
08:21 Proving a generalization of the Lemma
09:21 Version 2 of Proof: A invertible iff Det(A) nonzero
10:07 Main Theorem & Proof: Det(AB) = Det(A)Det(B)
12:26 Theorem & Proof: Determinant of the inverse of A is 1/Det(A)

Part of a series of lectures on Determinants of Matrices.
LA41 Definition of Determinant    • LA41 Determinants: Definition via Elementa...  
LA42 Determinant is Multi-linear and Alternating    • LA42 Determinant is Multi-linear and Alter...  
LA43 Determinants & Elementary Row Operations    • LA43 Determinants & Elementary Row Operations  
LA44 A invertible iff Det(A) nonzero; Det(AB) = Det(A)Det(B)    • LA44 A invertible iff Det(A) not zero; Det...  
LA45 Cofactor Expansion for Determinants

This is also 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.

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.