已知二次型经过正交变换化为标准形求参数a、b及所用的正交变换矩阵。

A . |t|<1 B . |t|≤1 C . t>0 D . t<0

A . 0 B . 1 C . 2 D . 不存在

A . 1 B . 3 C . 4 D . 5

A．｜A｜=｜B｜ B．｜A｜≠｜B｜ C．若｜A｜=0则｜B｜=0 D．若｜A｜＞0则｜B｜＞0

A．|A|=|B| B．|A|≠|B| C．若|A|=0则|B|=0 D．若|A|＞0则|B|＞0

已知ξ=[1,1,-1]^T是矩阵<img src='https://img2.soutiyun.com/ask/2021-03-05/983807677080177.png' />的一个特征向量. (1)确定参数a,b及ξ对应的特征值λ; (2)A是否相似于对角矩阵？说明理由。

若二阶实对称矩阵A与矩阵<img src='https://img2.soutiyun.com/ask/2020-12-21/977398837755134.png' />合同，则二次型X^TAX的标准形是________

将二次型<img src='https://img2.soutiyun.com/ask/2020-10-26/972557863460901.png' />化为标准形，并写出所用的线性变换。

如果实对称矩阵A与矩阵<img src='https://img2.soutiyun.com/ask/2020-08-20/966787469346466.png' />合同，则二次型x^TAx的规范形为(). A.<img src='https://img2.soutiyun.com/ask/2020-08-20/966787498718146.png' /> B.<img src='https://img2.soutiyun.com/ask/2020-08-20/966787513013964.png' /> C.<img src='https://img2.soutiyun.com/ask/2020-08-20/966787525690689.png' /> D.<img src='https://img2.soutiyun.com/ask/2020-08-20/966787536172288.png' />

已知二次型<img src='https://img2.soutiyun.com/ask/2021-01-01/978362209814944.png' />的秩等于1，求t的值。

<img src='https://img2.soutiyun.com/ask/2020-11-19/974647858740309.png' />

设二次型<img src='https://img2.soutiyun.com/ask/2020-10-26/972559849328486.jpg' />经正交变换x=Qy，化成<img src='https://img2.soutiyun.com/ask/2020-10-26/972559860523126.jpg' />试求常数a，b。

<img src='https://img2.soutiyun.com/ask/2020-12-29/978124353573357.png' />

A．2y21+y22-5y23 B．2y21+y22+5y23 C．y21+y22+5y23 D．2y21+y22+4y23

A．3 B．2 C．1 D．0

设A为n阶实对称矩阵，R(A)=n; 二次型 <img src='https://img2.soutiyun.com/ask/2020-12-17/977073420019754.png' /> (1)求二次型f的阵 (2) 二次型<img src='https://img2.soutiyun.com/ask/2020-12-17/977073445368204.png' />的规范形是否相同？说明理由.