求解下列非齐次线性方程组 2x1+3x2-x4=0 3x1+x2+5x3-4x4=2 7x2-10x3+5x4=-4 3x1-6x2+15x3-9x4=1

Question

求解下列非齐次线性方程组
2x1+3x2-x4=0
3x1+x2+5x3-4x4=2
7x2-10x3+5x4=-4
3x1-6x2+15x3-9x4=1

Answer 1

2 3 0 -1 0

3 1 5 -4 2
0 7 -10 5 -4
3 -6 15 -9 1 r4-r2,r2-r1
~
2 3 0 -1 0

1 -2 5 -3 2
7 0 -10 5 -4
0 -7 10 -5 -1 r1-2r2,r3-7r2
~
0 7 -10 5 -4

1 -2 5 -3 2
7 0 -10 5 -4
0 -7 10 -5 -1 r4+r1
~
0 7 -10 5 -4

1 -2 5 -3 2
7 0 -10 5 -4
0 0 0 0 -5
显然R(A)<R(A,b)，于是方程组无解