用克拉默法则解线性方程组X1-X2-X3-2X4= - 知识问答

用克拉默法则解线性方程组X1-X2-X3-2X4=-1,X1+X2-2X3+X4=1,X1+X2 =2‘,+X2+X3-

1个回答

X1-X2-X3-2X4=-1,
X1+X2-2X3+X4= 1,
X1+X2 =2,
+X2 +X3-X4 =1
D=
| 1 -1 -1 -2 |
| 1 1 -2 1 |
| 1 1 0 0 |
| 0 1 1 -1 |
=
| 1 -1 -1 -2 |
| 0 2 -1 3 |
| 0 2 1 2 |
| 0 1 1 -1 |
=
| 2 -1 3 |
| 2 1 2 |
| 1 1 -1 |
= ...
= -7
D1=
|-1 -1 -1 -2 |
| 1 1 -2 1 |
| 2 1 0 0 |
| 1 1 1 -1 |
= ...
= -9
D2=
| 1 -1 -1 -2 |
| 1 1 -2 1 |
| 1 2 0 0 |
| 0 1 1 -1 |
= ...
= -5
D3=
| 1 -1 -1 -2 |
| 1 1 1 1 |
| 1 1 2 0 |
| 0 1 1 -1 |
=...
= -5
D4=
| 1 -1 -1 -1 |
| 1 1 -2 1 |
| 1 1 0 2 |
| 0 1 1 1 |
= ...
= -3
x1=D1/D=9/7
x2=D2/D=5/7
x3=D3/D=5/7
x4=D4/D=3/7

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