?2???????5?????????????????将(?1,?2,?3)单位化得:p1??0?,p2?????1?????5????2???5????0??1?5?13053023026?16161??1??306????5???1,p??3??306??2??2??30??6?????, ?????Q???????????p1, p２, p３?????? ． ????八、（6分）设A是n阶正定矩阵，E是n阶单位矩阵，证明：E?A?1． 证明：因为A是正定矩阵，所以A的特征值?i?0(i?1,2,?,n)
方法一：又A?E的特征值为?1?1,?2?1,?,?n?1且?i?1?1(i?1,2,?,n)，
n 所以 A?E??i?1(?i?1)?1．
??1 ? ?２ T?1?方法二：因为存在正交阵Q使QAQ?QAQ?? ??? ?n???，??0(i?1,2,?,n)
i?????1+1 ??? ?２+1 ?Q?1，??0(i?1,?2,n,， 于是A?E?Q?i? ???? ??1n??n 所以A?E??i?1(?i?1)?1 ．
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