Row echelon form: Difference between revisions

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* The [[leading entry]] (that is, the left-most nonzero entry) of every nonzero row, called the '''pivot''', is on the right of the leading entry of every row above.<ref>{{harvtxt|Leon|2010|p=13}}:"A matrix is said to be in <strong>row echelon form</strong> ... (ii) If row {{mvar|k}} does not consist entirely of zeros, the number of leading zero entries in row <math>k + 1</math> is greater than the number of leading zero entries in row {{mvar|k}}."</ref>

Nihal seriously??

Some texts add the condition that the leading coefficient must be 1<ref>See, for instance, the first clause of the definition of row echelon form in {{harvtxt|Leon|2010|p=13}}: "A matrix is said to be in <strong>row echelon form</strong> (i) If the first nonzero entry in each nonzero row is 1."</ref> while others require this only in [[#Reduced row echelon form|reduced row echelon form]].

These two conditions imply that all entries in a column below a leading coefficient are zeros.<ref>{{harvnb|Meyer|2000|p=44}}</ref>