线性代数初等行变换求逆矩阵 0 1 0 0 0 0 2 0 0 0 0 3 4 0 0 0
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线性代数初等行变换求逆矩阵 0 1 0 0 0 0 2 0 0 0 0 3 4 0 0 0
线性代数初等行变换求逆矩阵 0 1 0 0 0 0 2 0 0 0 0 3 4 0 0 0
线性代数初等行变换求逆矩阵 0 1 0 0 0 0 2 0 0 0 0 3 4 0 0 0
(A,E) =
0 1 0 0 1 0 0 0
0 0 2 0 0 1 0 0
0 0 0 3 0 0 1 0
4 0 0 0 0 0 0 1
交换行得
4 0 0 0 0 0 0 1
0 1 0 0 1 0 0 0
0 0 2 0 0 1 0 0
0 0 0 3 0 0 1 0
r1*(1/4),r3*(2/3),r4*(1/3)
1 0 0 0 0 0 0 1/4
0 1 0 0 1 0 0 0
0 0 2 0 0 1/2 0 0
0 0 0 3 0 0 1/3 0
A^-1 =
0 0 0 1/4
1 0 0 0
0 1/2 0 0
0 0 1/3 0
解: (A,E) =
-1 0 1 4 1 0 0 0
0 1 -1 1 0 1 0 0
0 1 1 1 0 0 1 0
0 0 1 3 0 0 0 1
r2-r3, r1*(-1)
1 0 -1 -4 -1 0 0 0
0 1 -1 1 0 1 0 0
...
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解: (A,E) =
-1 0 1 4 1 0 0 0
0 1 -1 1 0 1 0 0
0 1 1 1 0 0 1 0
0 0 1 3 0 0 0 1
r2-r3, r1*(-1)
1 0 -1 -4 -1 0 0 0
0 1 -1 1 0 1 0 0
0 0 2 0 0 -1 1 0
0 0 1 3 0 0 0 1
r1 r4,r2 r4,r3-2r4
1 0 0 -1 -1 0 0 1
0 1 0 4 0 1 0 1
0 0 0 -6 0 -1 1 -2
0 0 1 3 0 0 0 1
r3*(-1/6),r1 r3,r2-4r3,r4-3r4
1 0 0 0 -1 1/6 -1/6 4/3
0 1 0 0 0 1/3 2/3 -1/3
0 0 0 1 0 1/6 -1/6 1/3
0 0 1 0 0 -1/2 1/2 0
r2
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