(1,2,1,3),(4,-1,-5,-6),(3,-3,-4,-7),(2,1,-1,0) 求向量组的轶和极大无关组

题目

(1,2,1,3),(4,-1,-5,-6),(3,-3,-4,-7),(2,1,-1,0) 求向量组的轶和极大无关组

答案

(a1,a2,a3,a4)=
1 4 3 2
2 -1 -3 1
1 -5 -4 -1
3 -6 -7 0
r2+2r3,r2+r3
3 -6 -5 0
3 -6 -7 0
1 -5 -4 -1
3 -6 -7 0
r7-r2,r2-r1
3 -6 -5 0
0 0 -2 0
1 -5 -4 -1
0 0 0 0
r2*(-1/2),r1+5r2
3 -6 0 0
0 0 1 0
1 -5 -4 -1
0 0 0 0
向量组的秩为3,a2,a3,a4是一个极大无关组.