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=== Echelon form of a matrix === | === Echelon form of a matrix === | ||
| − | A m X n matrix is in '''reduced row echelon form''' if it satisfies the following properties: | + | A m X n matrix is in '''row echelon form''' if it satisfies properties 1, 2, and 3. Furthermore A m X n matrix is in '''reduced row echelon form''' if it satisfies the following properties: |
1. If there are any zero rows, they must be at the bottom of the matrix. | 1. If there are any zero rows, they must be at the bottom of the matrix. | ||
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2. The first nonzero entry from the left of a nonzero row is a 1, which is also called the '''leading one''' of that row. | 2. The first nonzero entry from the left of a nonzero row is a 1, which is also called the '''leading one''' of that row. | ||
| − | 3. | + | 3. The leading one for each nonzero row appears to the right and below any leading ones in the previous rows. |
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| + | 4. For a column with a leading one, the other entries in that column are zero. | ||
Revision as of 13:04, 14 December 2012
Echelon form of a matrix
A m X n matrix is in row echelon form if it satisfies properties 1, 2, and 3. Furthermore A m X n matrix is in reduced row echelon form if it satisfies the following properties:
1. If there are any zero rows, they must be at the bottom of the matrix.
2. The first nonzero entry from the left of a nonzero row is a 1, which is also called the leading one of that row.
3. The leading one for each nonzero row appears to the right and below any leading ones in the previous rows.
4. For a column with a leading one, the other entries in that column are zero.
