用初等变换求321315323矩阵的逆矩阵
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用初等变换求321315323矩阵的逆矩阵
![用初等变换求321315323矩阵的逆矩阵](/uploads/image/z/18731683-19-3.jpg?t=%E7%94%A8%E5%88%9D%E7%AD%89%E5%8F%98%E6%8D%A2%E6%B1%82321315323%E7%9F%A9%E9%98%B5%E7%9A%84%E9%80%86%E7%9F%A9%E9%98%B5)
(A,E) =
3 2 1 1 0 0
3 1 5 0 1 0
3 2 3 0 0 1
r2-r1,r3-r1
3 2 1 1 0 0
0 -1 4 -1 1 0
0 0 2 -1 0 1
r1*(1/3),r2*(-1),r3*(1/2)
1 2/3 1/3 1/3 0 0
0 1 -4 1 -1 0
0 0 1 -1/2 0 1/2
r1-(1/3)r3,r2+4r3
1 2/3 0 1/2 0 -1/6
0 1 0 -1 -1 2
0 0 1 -1/2 0 1/2
r1-(2/3)r2
1 0 0 7/6 2/3 -3/2
0 1 0 -1 -1 2
0 0 1 -1/2 0 1/2
A^-1 =
7/6 2/3 -3/2
-1 -1 2
-1/2 0 1/2
3 2 1 1 0 0
3 1 5 0 1 0
3 2 3 0 0 1
r2-r1,r3-r1
3 2 1 1 0 0
0 -1 4 -1 1 0
0 0 2 -1 0 1
r1*(1/3),r2*(-1),r3*(1/2)
1 2/3 1/3 1/3 0 0
0 1 -4 1 -1 0
0 0 1 -1/2 0 1/2
r1-(1/3)r3,r2+4r3
1 2/3 0 1/2 0 -1/6
0 1 0 -1 -1 2
0 0 1 -1/2 0 1/2
r1-(2/3)r2
1 0 0 7/6 2/3 -3/2
0 1 0 -1 -1 2
0 0 1 -1/2 0 1/2
A^-1 =
7/6 2/3 -3/2
-1 -1 2
-1/2 0 1/2