Chapter 2.3 Determinants-Properties

Then the following are equivalent they are all true

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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.

Ask a homework question - tutors are online