Question

用克莱姆法则解线性方程组

x1+x2-2x3=-3
2x1+x2-x3=1
x1-x2+3x3=8
求详细过程

Answer 1

解:
D =
1 1 -2
2 1 -1
1 -1 3
= 1

D1 =
-3 1 -2
1 1 -1
8 -1 3
= 1

D2 =
1 -3 -2
2 1 -1
1 8 3
= 2

D3 =
1 1 -3
2 1 1
1 -1 8
= 3

所以 x1 = D1/D = 1
x2 = D2/D = 2
x3 = D3/D = 3

Answer 2

其实就是求几个行列式.
| -3 1 -2 | | 1 1 -2 |
x1= | 1 1 -1 | / | 2 1 -1 |
| 8 -1 3 | | 1 -1 3 |

| 1 -3 -2 | | 1 1 -2 |
x2= | 2 1 -1 | / | 2 1 -1 |
| 1 8 3 | | 1 -1 3 |

| 1 1 -3 | | 1 1 -2 |
x3= | 2 1 1 | / | 2 1 -1 |
| 1 -1 8 | | 1 -1 3 |

Answer 3