Question

求非齐次方程组的解 x1+x2+x3=0 x1+x2-x3-x4-2x5=1 2x1+2x2-x4-2x5=1 5x1+5x2-3x3-4x4-8x5=4

Answer 1

解: 增广矩阵 =
1 1 1 0 0 0
1 1 -1 -1 -2 1
2 2 0 -1 -2 1
5 5 -3 -4 -8 4
r2-r1,r3-2r1,r4-5r1
1 1 1 0 0 0
0 0 -2 -1 -2 1
0 0 -2 -1 -2 1
0 0 -8 -4 -8 4
r3-r2,r4-4r2,r2*(-1/2)
1 1 1 0 0 0
0 0 1 1/2 1 -1/2
0 0 0 0 0 0
0 0 0 0 0 0
r1-r2
1 1 0 -1/2 -1 1/2
0 0 1 1/2 1 -1/2
0 0 0 0 0 0
0 0 0 0 0 0
通解为: (1/2,0,1/2,0,0)'+c1(-1,1,0,0,0)'+c2(1,0,-1,2,0)'+c3(1,0,-1,0,1)