Lecture 25 - Mar 9

Lecture 25 - Mar 9 - Monday March 9 Lecture 25 : Elementary...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: Monday March 9 Lecture 25 : Elementary matrices and invertibility . (Refers to 3.6) Expectations: 1. Define row-equivalent matrices. 2. Recognize that a square matrix A is invertible iff A is row-equivalent to I n . 3. Define elementary matrix. 4. Recognize that for any two row-equivalent matrices A and B , there exist and invertible matrix P such that A = PB . 25.1 Definition Row-equivalent matrices . Two matrices A and B are row-equivalent if there is a finite sequence of elementary row operations that can be applied to A to obtain the matrix B . (Hence row-equivalent matrices both reduce to the same RREF. Why?) We sometimes use the notation A ~ B , to say A is row-equivalent to B . 25.1.1 Example The following chain of ERO's applied to A show shows that A is row-equivalent to B . 0 1 0 1 1 2 1 5 1 2 1 5 1 2 1 5 A = 1 2 1 5 0 1 0 1 0 1 0 1 0 1 0 1 = B 2 2 2 6 P 12 2 2 2 6 (1/2)R 3 1 1 1 3 1R 1 + R 3 0 1 0 2 25.2 Definition An " elementary matrix " is a square matrix E m m obtained by applying a SINGLE elementary row operation to I m . 25.2.1 There are 3 types of elementary matrices, E Pij , E cR i , E cR i + R j . Each is obtained by applying one of the 3 elementary row operations of type I, II, or II respectively to I m ....
View Full Document

This note was uploaded on 06/10/2010 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

Page1 / 5

Lecture 25 - Mar 9 - Monday March 9 Lecture 25 : Elementary...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online