Sistema
Escalonado
É todo sistema no qual:
a) as incógnitas das equações lineares estão escritas numa mesma ordem;
b) em cada equação há pelo menos um coeficiente não nulo;
c) o número de coeficientes nulos aumenta de equação para equação.
Exemplo:
![](data:image/png;base64,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)
É todo sistema no qual:
a) as incógnitas das equações lineares estão escritas numa mesma ordem;
b) em cada equação há pelo menos um coeficiente não nulo;
c) o número de coeficientes nulos aumenta de equação para equação.
Exemplo:
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