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用正交变换化二次型?
3.
2?2?2?2?
f?x?x?x?x?2?x?x?2?x?x?2?x?x?2?x?x?2?x?x?2?x?x?
1?2?3?4?1?2?1?3?1?4?2?3?2?4?3?4?
.?
为标准形?
若二次型?
4.?
2?2?2?
f?(?x?,?x?,?x?)?(?k?1?)?x?(?k?1?)?x?(?k?2?)?x?
1?2?3?1?2?3?
,?k?.?
为正定二次型求的取值范围
1?
5.?
A
设三阶实对称矩阵?的特征值为,4?.?
1?2?3?
2?
(1)?证明:?2?E?A?是可逆矩阵??
2?
(2)?B?(?A?)?4?A?4?E?,?B?.?
设试证是正定矩阵 |
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