3x1+4x2-5x3+7x4=0 2x1-3x2+3x3-2x4=0 4x1+11x2-13x3+16x4=0 7x1-2x2+x3+3x4=0 解方程组,用矩阵的方法

系数矩阵 A =
3 4 -5 7
2 -3 3 -2
4 11 -13 16
7 -2 1 3
r1-r2,r3-2r2
-->
1 7 -8 9
2 -3 3 -2
0 17 -19 20
7 -2 1 3
r2-2r1,r4-7r1
-->
1 7 -8 9
0 -17 19 -20
0 17 -19 20
0 -51 57 60
r3+r2,r4-3r2,r2*(-1/17)
1 7 -8 9
0 1 -19/17 20/17
0 0 0 0
0 0 0 0
r1-7r2
1 0 -3/17 13/17
0 1 -19/17 20/17
0 0 0 0
0 0 0 0
方程组的通解为:c1(3,19,17,0)+c2(13,20,0,-17).