1.2 - 1.2 Row Reduction and Echelon Forms Definition: The...

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Unformatted text preview: 1.2 Row Reduction and Echelon Forms Definition: The leading entry of a row in a matrix is the first non-zero 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 non-zero rows are above any zero rows 2. The leading non-zero entry in any row is to the right of that of the previous row 3. All entries in a column below a leading non-zero entry are zero The matrix is in reduced (row) echelon form if it also satisfies 4. The leading non-zero entry in each non-zero row is 1 5. Each leading 1 is the only non-zero 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...
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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.

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1.2 - 1.2 Row Reduction and Echelon Forms Definition: The...

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