Question

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

Answer 1

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.