Statistics and Probability Glossary
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Reduced Row Echelon FormA
matrix
is in row echelon form (ref)
when it satisfies the following conditions.
- The first non-zero element in each row, called the
leading entry, is 1.
- Each leading entry is in a column to the right of the
leading entry in the previous row.
- Rows with all zero elements, if any, are below rows having a
non-zero element.
A matrix is in reduced row echelon form (rref)
when it satisfies the following conditions.
- The matrix is in row echelon form (i.e., it satisfies the
three conditions listed above).
- The leading entry in each row is the only non-zero entry in
its column.
A matrix in echelon form is called an echelon matrix.
Matrix A and matrix B are examples
of echelon matrices.
|
1 |
2 |
3 |
4 |
|
| 0 |
0 |
1 |
3 |
| 0 |
0 |
0 |
1 |
| 0 |
0 |
0 |
0 |
|
|
|
1 |
2 |
0 |
0 |
|
| 0 |
0 |
1 |
0 |
| 0 |
0 |
0 |
1 |
| 0 |
0 |
0 |
0 |
|
| A |
|
B |
Matrix A is in row echelon form, and matrix B
is in reduced row echelon form. |