高等数学 矩阵
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解: (A,E) =
1 2 0 0 1 0 0 0
0 1 0 2 0 1 0 0
0 0 1 0 0 0 1 0
0 0 2 1 0 0 0 1
r4-2r3
1 2 0 0 1 0 0 0
0 1 0 2 0 1 0 0
0 0 1 0 0 0 1 0
0 0 0 1 0 0 -2 1
r2-2r4
1 2 0 0 1 0 0 0
0 1 0 0 0 1 4 -2
0 0 1 0 0 0 1 0
0 0 0 1 0 0 -2 1
r1-2r2
1 0 0 0 1 -2 -8 4
0 1 0 0 0 1 4 -2
0 0 1 0 0 0 1 0
0 0 0 1 0 0 -2 1
A^-1 =
1 -2 -8 4
0 1 4 -2
0 0 1 0
0 0 -2 1
1 2 0 0 1 0 0 0
0 1 0 2 0 1 0 0
0 0 1 0 0 0 1 0
0 0 2 1 0 0 0 1
r4-2r3
1 2 0 0 1 0 0 0
0 1 0 2 0 1 0 0
0 0 1 0 0 0 1 0
0 0 0 1 0 0 -2 1
r2-2r4
1 2 0 0 1 0 0 0
0 1 0 0 0 1 4 -2
0 0 1 0 0 0 1 0
0 0 0 1 0 0 -2 1
r1-2r2
1 0 0 0 1 -2 -8 4
0 1 0 0 0 1 4 -2
0 0 1 0 0 0 1 0
0 0 0 1 0 0 -2 1
A^-1 =
1 -2 -8 4
0 1 4 -2
0 0 1 0
0 0 -2 1
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