利用初等行变换化下列矩阵为行最简矩阵［231-3-7120-2-43-28302-3利用初等行变换化下列矩阵为行最简矩阵［231-3-7120-2-43-28302-3743］

Question

利用初等行变换化下列矩阵为行最简矩阵 ［231-3-7 120-2-4 3-2830 2-3
利用初等行变换化下列矩阵为行最简矩阵 ［231-3-7 120-2-4 3-2830 2-3743］

Answer 1

r1-2r2,r3-3r2,r4-2r2
0 -1 1 1 1
1 2 0 -2 -4
0 -8 8 9 12
0 -7 7 8 11
r1*(-1),r2-2r1,r3+8r1,r4+7r1
0 1 -1 -1 -1
1 0 2 0 -2
0 0 0 1 4
0 0 0 1 4
r1+r3,r4-r3
0 1 -1 0 3
1 0 2 0 -2
0 0 0 1 4
0 0 0 0 0
r1r2
1 0 2 0 -2
0 1 -1 0 3
0 0 0 1 4
0 0 0 0 0
此为行最简形.