Question

线性代数求解。高手出来啊 ！！！

1： x1+x2-2x4=2
2x1+3x2-2x3-x4=6
3x1+4x2-x3=3
2:x1+2x2+2x3+x4=0
2x1+x2-2x3-4x4=0
x1+x2-x3-3x4=0
x2+3x3+4x4=0

3:判断下列方程是否有解
x1-2x2+3x3-x4=1
3x1-x2+5x3-3x4=2
2x1+x2+2x3-2x4=3

Answer 1

解:增广矩阵=
1 1 0 -2 2
2 3 -2 0 6
3 4 -1 0 3

r3-r2
1 1 0 -2 2
2 3 -2 0 6
1 1 1 0 -3

r1-r3,r2-2r3
0 0 -1 -2 5
0 1 -4 0 12
1 1 1 0 -3

r1*(-1),r2+4r1,r3-r1
0 0 1 2 -5
0 1 0 8 -8
1 1 0 -2 2

r3-r2
0 0 1 2 -5
0 1 0 8 -8
1 0 0 -10 10

r1<->r3
1 0 0 -10 10
0 1 0 8 -8
0 0 1 2 -5

通解为: (10,-8,-5,0)'+c(10,-8,-2,1)
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2. 解: 系数矩阵 =
1 2 2 1
2 1 -2 -4
1 1 -1 -3
0 1 3 4

r1-2r4,r2-r4,r3-r4
1 0 -4 -7
2 0 -5 -8
1 0 -4 -7
0 1 3 4

r2-2r1,r3-r1
1 0 -4 -7
0 0 3 6
0 0 0 0
0 1 3 4

r4-r3,r2*(1/3),r1+4r2
1 0 0 1
0 0 1 2
0 0 0 0
0 1 0 -2

交换行
1 0 0 1
0 1 0 -2
0 0 1 2
0 0 0 0

通解为: c(-1,2,-2,1)'.
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3:判断下列方程是否有解
x1-2x2+3x3-x4=1
3x1-x2+5x3-3x4=2
2x1+x2+2x3-2x4=3

解: 增广矩阵 =
1 -2 3 -1 1
3 -1 5 -3 2
2 1 2 -2 3

r2-r1-r3
1 -2 3 -1 1
0 0 0 0 -2
2 1 2 -2 3

方程组无解.

Answer 2

看来矩阵没有学好啊