Reduced row echelon form of matrix

bimal
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How do you know, when you have to stop row-equivalent operations when you are trying to get a 'reduced row-echelon' form of a given matrix. Is it necessary to have all the columns with pivot element as 1 and rest as 0? do you need to continue the operation if you already have a all 0 row? I want to use the number of columns with pivot element as 1 to determine the linearly indendent columns.
 
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A reduced row echelon form matrix has "1" as the leading entry in each nonzero row, and each leading 1 is the only nonzero entry in its column. As well each leading entry of a row is in a column to the right of the leading entry of the row above it.
 

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