This preview shows page 1. Sign up to view the full content.
Unformatted text preview: trix. Then the following are equivalent
(they are all true or they are all false).
(a) A is invertible.
(b) Ax = 0 has only the trivial solution.
(c) rref (A) = In .
(d) A = E1 E2 . . . Er for some elementary matrices E1 , E2 , . . . , Er .
(e) Ax = b has exactly one solution for every n × 1 column vector
b.
(f) det A = 0. Outline Linearity of the Determinant Determinants and Invertibility Determinants and Products Determinants and Inverses The Determinant of a Product with an Elementary Matrix
Theorem
If A is an n × n matrix and E is an n × n elementary matrix, then
det(EA) = (det E )(de...
View
Full
Document
This note was uploaded on 02/10/2014 for the course MATH 2270 taught by Professor Kenyonj.platt during the Spring '14 term at Snow College.
 Spring '14
 KenyonJ.Platt
 Linear Algebra, Algebra, Determinant

Click to edit the document details