...A*为A的伴随矩阵,|A|>0,P为三阶可逆矩阵,P的第一列为(1,1,-1)T...
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发布时间：2024-07-04 04:00
共1个回答
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时间：2024-08-05 04:41
（I）
∵P-1A*P=1000?2000?2，而P可逆，
∴|A*|=4，
而|A*|=|A|n-1=|A|2，
故：|A|=2，
由P-1A*P，知A*的特征值分别为1、-2、-2，
且特征值1所对应的特征向量是p的第一列（1，1，-1）T，
又∵A为实对称阵，
∴A*也是实对称矩阵，
而对称矩阵的不同特征值所对应的特征向量是正交的，
设-2所对应的特征向量为：x1x2x3，
则：
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