Question

解线性方程组（1）2x1-x2+x3-2x4=7 （2）x1+2x2-3x3=-4 （3）-x1-x2+x3+4x4=4

Answer 1

增广矩阵 =

2 -1 1 -2 7

1 2 -3 0 -4

-1 -1 1 4 4

3 1 -1 -6 0

r1+2r3,r2+r3,r4+3r3,r3*(-1)

0 -3 3 6 15

0 1 -2 4 0

1 1 -1 -4 -4

0 -2 2 6 12

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

0 0 -3 18 15

0 1 -2 4 0

1 0 1 -8 -4

0 0 -2 14 12

r1*(-1/3),r2+2r1,r3-r1,r4+2r1

0 0 1 -6 -5

0 1 0 -8 -10

1 0 0 -2 1

0 0 0 2 2

r1+3r4,r2+4r4,r3+r4,r4*(-1/2)

0 0 1 0 1

0 1 0 0 -2

1 0 0 0 3

0 0 0 1 1

r1r3

1 0 0 0 3

0 1 0 0 -2

0 0 1 0 1

0 0 0 1 1

所以方程组有唯一解:(3,-2,1,1)'