Question

求线性方程组的解：2x1+3x2+x3=4x1-2x2+4x3=-53x1+8x2-3x3=134x1-x2+9x3=-

Answer 1

解: 增广矩阵 =

2 3 1 4

1 -2 4 -5

3 8 -2 13

4 -1 9 -6

r1-2r2,r3-3r2,r4-4r2

0 7 -7 14

1 -2 4 -5

0 14 -14 28

0 7 -7 14

r3-2r1,r4-r1,r1*(1/7),r2+2r1

0 1 -1 2

1 0 2 -1

0 0 0 0

0 0 0 0

r1r2

1 0 2 -1

0 1 -1 2

0 0 0 0

0 0 0 0

通解为: (-1,2,0)^T+c(2,-1,-1)^T.