This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1.2 Row Reduction and Echelon Forms Definition: The leading entry of a row in a matrix is the first nonzero entry in that row from the left. EX: 1 2 3 0 2 2 0 5 1 Definition: A matrix A is in (row) echelon form if 1. All nonzero rows are above any zero rows 2. The leading nonzero entry in any row is to the right of that of the previous row 3. All entries in a column below a leading nonzero entry are zero The matrix is in reduced (row) echelon form if it also satisfies 4. The leading nonzero entry in each nonzero row is 1 5. Each leading 1 is the only nonzero entry in its column. 1 EX: 1 2 3 0 0 2 0 0 0 REF RREF 1 2 0 0 0 1 0 0 0 REF ? RREF ? We illustrate the standard method for bringing a ma trix to RE or RRE using elementary row operations A = 2 1 9 2 6 2 0 2 2 6 2 2 3 9 2 2 19 R 1 R 2  2 6 2 0 2 2 1 9 2 6 2 2 3 9 2 2 19 pivot position R 1  1 2 R 1 0 1 3 1 0 1 0 0 0 2 1 9 0 2 6 2 2 0 3 9 2 2 19 2 R 3 R 3 2 R 1 R 4 R 4 3 R 1 0 1 3 1 0 1 0 0 0 2 1 9 0 0 0 0 2 2 0 0 0 5 2 22 R 2 1 2 R 2 R 3 1 2 R 3 0 1 3 1 0 1 0 0 0 1 1 2 9 2 0 0 0 0 1 1 0 0 0 5 2 22 R 4 R 4 5 R 2...
View
Full
Document
This note was uploaded on 04/09/2011 for the course MATH 232 taught by Professor Russel during the Spring '10 term at Simon Fraser.
 Spring '10
 Russel
 Linear Algebra, Algebra

Click to edit the document details