线性代数基础，求解如图逆矩阵问题
2个回答
北京埃德思远电气技术咨询有限公司
2021-11-22 广告
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A =
[B O]
[O C]
其中 B =
[1 2]
[2 -1]
C =
[1 0]
[3 2]
B^(-1) = (-1/5)*
[-1 -2]
[-2 1]
=
[1/5 2/5]
[2/5 -1/5]
B^2 = 5E, B^4 = 25E
C^(-1) = (1/2)*
[ 2 0]
[-3 1]
=
[ 1 0]
[-3/2 1/2]
C^2 =
[1 0]
[9 4]
C^4 =
[1 0]
[45 16]
A^(-1) =
[B^(-1) O]
[O C^(-1)]
=
[1/5 2/5 0 0]
[2/5 -1/5 0 0]
[ 0 0 1 0]
[ 0 0 -3/2 1/2]
|A^T| = |A| = |B||C| = (-5)2 = -10
A^4 =
[B^4 O]
[O C^4]
[B O]
[O C]
其中 B =
[1 2]
[2 -1]
C =
[1 0]
[3 2]
B^(-1) = (-1/5)*
[-1 -2]
[-2 1]
=
[1/5 2/5]
[2/5 -1/5]
B^2 = 5E, B^4 = 25E
C^(-1) = (1/2)*
[ 2 0]
[-3 1]
=
[ 1 0]
[-3/2 1/2]
C^2 =
[1 0]
[9 4]
C^4 =
[1 0]
[45 16]
A^(-1) =
[B^(-1) O]
[O C^(-1)]
=
[1/5 2/5 0 0]
[2/5 -1/5 0 0]
[ 0 0 1 0]
[ 0 0 -3/2 1/2]
|A^T| = |A| = |B||C| = (-5)2 = -10
A^4 =
[B^4 O]
[O C^4]
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