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考研
设A为四阶矩阵,|A*|=8,则|(1/4A)-1-3A*|=________.
设A为四阶矩阵,|A*|=8,则|(1/4A)-1-3A*|=________.
admin
2022-11-03
321
问题
设A为四阶矩阵,|A
*
|=8,则|(1/4A)
-1
-3A
*
|=________.
选项
答案
8
解析
因为A为四阶矩阵,且|A
*
|=8,所以|A
*
|=|A|
3
=8,于是|A|=2.又AA
*
=|A|E=2E,所以A
*
=2A
-1
,故|(1/4A)
-1
-3A
*
|=|4A
-1
-6A
-1
|=|(-2)A
-1
|=(-2)
4
|A
-1
|=16×1/2=8.
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0
考研数学三
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