Question

用线代解线性方程组①6x1-2x2-3x5=3 ② x1-x2+x4-x5=1 ③ 2x1+x3-x5=2 ④ x1-x

Answer 1

解: 增广矩阵 =

6 -2 0 0 -3 3

1 -1 0 1 -1 1

2 0 1 0 -1 2

1 -1 -2 -1 0 -2

r1-6r2,r3-2r2,r4-r2

0 4 0 -6 3 -3

1 -1 0 1 -1 1

0 2 1 -2 1 0

0 0 -2 -2 1 -3

r1-2r3

0 0 -2 -2 1 -3

1 -1 0 1 -1 1

0 2 1 -2 1 0

0 0 -2 -2 1 -3

r4-r1,r1*(-1/2),r3-r1

0 0 1 1 -1/2 3/2

1 -1 0 1 -1 1

0 2 0 -3 3/2 -3/2

0 0 0 0 0 0

r3*1/2,r2+r3

0 0 1 1 -1/2 3/2

1 0 0 -1/2 -1/4 1/4

0 1 0 -3/2 3/4 -3/4

0 0 0 0 0 0

交换行

1 0 0 -1/2 -1/4 1/4

0 1 0 -3/2 3/4 -3/4

0 0 1 1 -1/2 3/2

0 0 0 0 0 0

方程组的通解为 (1/4,-3/4,3/2,0,0)^T + k1(1,3,-2,2,0)^T +k2(1,-3,2,0,4)^T.