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用初等变换求下列矩阵的逆矩阵(2100)(3200)(5718)(-1-3-1-1)
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用初等变换求下列矩阵的逆矩阵(2100)(3200)(5718)(-1-3-1-1)
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答案和解析
(A,E)=
2 1 0 0 1 0 0 0
3 2 0 0 0 1 0 0
5 7 1 8 0 0 1 0
-1 -3 -1 -1 0 0 0 1
r2-2r1, r4+r3
2 1 0 0 1 0 0 0
-1 0 0 0 -2 1 0 0
5 7 1 8 0 0 1 0
4 4 0 7 0 0 1 1
r1+2r2, r2*(-1)
0 1 0 0 -3 2 0 0
1 0 0 0 2 -1 0 0
5 7 1 8 0 0 1 0
4 4 0 7 0 0 1 1
r1r2
1 0 0 0 2 -1 0 0
0 1 0 0 -3 2 0 0
5 7 1 8 0 0 1 0
4 4 0 7 0 0 1 1
r3-5r1-7r2,r4-4r1-4r2
1 0 0 0 2 -1 0 0
0 1 0 0 -3 2 0 0
0 0 1 8 11 -9 1 0
0 0 0 7 4 -4 1 1
r4*(1/7),r3-8r4
1 0 0 0 2 -1 0 0
0 1 0 0 -3 2 0 0
0 0 1 0 45/7 -31/7 -1/7 -8/7
0 0 0 1 4/7 -4/7 1/7 1/7
A^-1=
2 -1 0 0
-3 2 0 0
45/7 -31/7 -1/7 -8/7
4/7 -4/7 1/7 1/7
2 1 0 0 1 0 0 0
3 2 0 0 0 1 0 0
5 7 1 8 0 0 1 0
-1 -3 -1 -1 0 0 0 1
r2-2r1, r4+r3
2 1 0 0 1 0 0 0
-1 0 0 0 -2 1 0 0
5 7 1 8 0 0 1 0
4 4 0 7 0 0 1 1
r1+2r2, r2*(-1)
0 1 0 0 -3 2 0 0
1 0 0 0 2 -1 0 0
5 7 1 8 0 0 1 0
4 4 0 7 0 0 1 1
r1r2
1 0 0 0 2 -1 0 0
0 1 0 0 -3 2 0 0
5 7 1 8 0 0 1 0
4 4 0 7 0 0 1 1
r3-5r1-7r2,r4-4r1-4r2
1 0 0 0 2 -1 0 0
0 1 0 0 -3 2 0 0
0 0 1 8 11 -9 1 0
0 0 0 7 4 -4 1 1
r4*(1/7),r3-8r4
1 0 0 0 2 -1 0 0
0 1 0 0 -3 2 0 0
0 0 1 0 45/7 -31/7 -1/7 -8/7
0 0 0 1 4/7 -4/7 1/7 1/7
A^-1=
2 -1 0 0
-3 2 0 0
45/7 -31/7 -1/7 -8/7
4/7 -4/7 1/7 1/7
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