Definition of Reduced Row Echelon Form

Row Echelon Form :        Rules 1 - 3.
Reduced Row Echelon Form: Rules 1 - 5.
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Leading entry: The first nonzero entry in a row.
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1. All entries below a leading entry are zero.

2. The leading entry in row i is to the right of
   the leading entry in row (i-1).

3. Rows of all zeros, if any, are grouped at the bottom.
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4. The leading entry in each row is 1.

5. All entries above a leading entry are zero.