行阶梯形形式

行阶梯形形式(row echelon form)

行阶梯形形式需要满足一下三个条件

(1)If the first nonzero entry in each nonzero row is 1.

每个非0行的第一个非零项为1

(2)If row k does not consist entirely of zeros,the number of leading zero entries in row k+1 is greater than the number of leading zero entries in row k.

如果第k行并非全为0，则第k+1行领衔0的数量要比第k行的多

(3)If there are rows whose entries are all zero,they are below the rows having nonzero entries.

如果有某些行的元素全部为0，他们都在含非零行的下面

The process of using row operations1,2and3 to transform a linear system into one whose augmented

matrix is in row echelon form is calledGaussian elimination

以1，2或3类变化使得一个增广线性系统变为行阶梯性形式的方法叫做高斯消元法