Question

高等代数，第二题怎么做，帮帮忙

Answer 1

使用初等行变换
2 -1 -1 1 2
1 1 -2 1 4
4 -6 2 -2 4
3 6 -9 7 9 r1-2r2,r3-4r2,r4-3r2
~
0 -3 3 -1 -6
1 1 -2 1 4
0 -10 10 -6 -12
0 3 -3 4 -3 r1+r4，交换行次序
~
1 1 -2 1 4
0 0 0 3 -9
0 -10 10 -6 -12
0 3 -3 4 -3 r2/3,r1-r2,r3+6r2,r4-4r2
~
1 1 -2 0 7
0 0 0 1 -3
0 -10 10 0 -30
0 3 -3 0 9 r3/(-10),r1-r3,r4-3r3,交换r2、r3
~
1 0 -1 0 4
0 1 -1 0 3
0 0 0 1 -3
0 0 0 0 0
于是极大无关组为c1,c2,c4
而c3=-c1-c2，c5=4c1+3c2-3c4