Question

如何将这两个矩阵化为行最简形矩阵

1 1 1
2 3 0
1 0 2
和
0 0 -1
1 4 -1
-1 -4 2
请写出具体步骤（各步初等变换），谢谢

Answer 1

(1)
1 1 1
2 3 0
1 0 2

r2-2r1,r3-r1
1 1 1
0 1 -2
0 -1 1

r1-r2,r3+r2
1 0 3
0 1 -2
0 0 -1

r3*(-1),r1-3r3,r2+2r3
1 0 0
0 1 0
0 0 1

(2)
0 0 -1
1 4 -1
-1 -4 2

r3+r2
0 0 -1
1 4 -1
0 0 1

r1*(-1),r2+r1,r3-r1
0 0 1
1 4 0
0 0 0

r1<->r2
1 4 0
0 0 1
0 0 0