A= 1 -1 2 1 0 2 -2 4 2 0 3 0 6 -1 1 0 3 0 0 1 怎么化为最简行阶梯形矩阵?

问题描述:

A= 1 -1 2 1 0 2 -2 4 2 0 3 0 6 -1 1 0 3 0 0 1 怎么化为最简行阶梯形矩阵?
A= ( 1 -1 2 1 0) (2 -2 4 2 0 ) (3 0 6 -1 1) (0 3 0 0 1)

r2-2r1,r3-3r1
1 -1 2 1 0
0 0 0 0 0
0 3 0 -4 1
0 3 0 0 1
r4-r3
1 -1 2 1 0
0 0 0 0 0
0 3 0 -4 1
0 0 0 4 0
交换行得
1 -1 2 1 0
0 3 0 -4 1
0 0 0 4 0
0 0 0 0 0
-->
1 0 2 0 1/3
0 1 0 0 1/3
0 0 0 1 0
0 0 0 0 0