1. Linear Algebra---Meiling CHEN
Lecture 18
Determinants det(A) square matrix
Properties
NUU Department of Electrical Engineering
Linear Algebra---Meiling CHEN

2. Linear Algebra---Meiling CHEN
Properties :
Exchange rows reverse sign of det
2 equal rows  det=0 (exchange rows get same matrix only probability is 0)
Linear for each row
NUU Department of Electrical Engineering
Linear Algebra---Meiling CHEN

3. Linear Algebra---Meiling CHEN
Subtract l*row i from row j det does not change
6 row of zeros  det(A)=0 7.
Product of Pivots
One of advantage of LU factorization
By elimination we can kill these
NUU Department of Electrical Engineering
Linear Algebra---Meiling CHEN

4. Linear Algebra---Meiling CHEN
when A is singular
when A is invertible 9
10.
Zero row
A=LU
NUU Department of Electrical Engineering
Linear Algebra---Meiling CHEN