3 5 1 4 （二阶行列式）用代数余子式求他的逆矩阵..我用代数余子式算出来不对..._数学解答

3 5 1 4 （二阶行列式）用代数余子式求他的逆矩阵..我用代数余子式算出来不对...

人气：196 ℃　时间：2019-10-14 07:33:52

解答

A=
3 5
1 4
|A| = 3*4-5*1 = 7
A11 = (-1)^(1+1) * 4 = 4
A12 = (-1)^(1+2) * 1 = -1
A21 = (-1)^(2+1) * 5 = -5
A22 = (-1)^(2+2) * 3 = 3
A^-1 = (1/|A|) A* = (1/7) *
A11 A21
A12 A22
= (1/7) *
4 -5
-1 3
=
4/7 -5/7
-1/7 3/7