求{X1-3X2+X3-2X4=0；-5X1+X2-2X3+3X4=0；-X1-11X2+2X3-5X4=0；3X1+5X2+X4=0
问题描述：
求{X1-3X2+X3-2X4=0；-5X1+X2-2X3+3X4=0；-X1-11X2+2X3-5X4=0；3X1+5X2+X4=0
答
解: 增广矩阵 =
1 -3 1 -2
-5 1 -2 3
-1 -11 2 -5
3 5 0 1
r2+5r1,r3+r1,r4-3r1
1 -3 1 -2
0 -14 3 -7
0 -14 3 -7
0 14 -3 7
r2+r4,r3+r4
1 -3 1 -2
0 0 0 0
0 0 0 0
0 14 -3 7
r4*(1/14), r1+3r4
1 0 5/14 -1/2
0 0 0 0
0 0 0 0
0 1 -3/14 1/2
方程组的通解为: c1(5,-3,-14,0)'+c2(1,-1,0,2),c1,c2为任意常数.