判断齐次线性方程组的解 x1+x2+2x3+3x4=0 x1+2x2+3x3-x4=0 2x1-x2-x3-2x4=0 2x1+3x2-x3-x4=0
问题描述：
判断齐次线性方程组的解 x1+x2+2x3+3x4=0 x1+2x2+3x3-x4=0 2x1-x2-x3-2x4=0 2x1+3x2-x3-x4=0
答
系数矩阵A=
1 1 2 3
1 2 3 -1
2 -1 -1 -2
2 3 -1 -1
r2-r1,r3-2r1,r4-2r1
1 1 2 3
0 1 1 -4
0 -3 -5 -8
0 1 -5 -7
r3+3r2,r4-r2
1 1 2 3
0 1 1 -4
0 0 -2 -20
0 0 -6 -3
r4-3r3
1 1 2 3
0 1 1 -4
0 0 -2 -20
0 0 0 57
所以方程组只有零解.