问题 问答题

设A为3阶实对称矩阵,A的秩为2,且


求A的所有特征值与特征向量;

答案

参考答案:因秩r(A)=2,知|A|=0,所以λ=0是A的特征值.又由分块矩阵乘法,有
[*]
按特征值定义,知λ=-1是A的特征值,[*],k1≠0是A属于λ=-1的特征向量.
λ=1是A的特征值,且属于λ=1的特征向量为[*]
设[*]是A的属于λ=0的特征向量,由于A是实对称矩阵,特征值不同特征向量相互正交,故
[*]
于是矩阵A属于λ=0的特征向量为[*]

阅读理解

阅读理解

     You want to know about my staying in America, right? Well, to tell you the truth, it is really an eye-opening

experience to study here.

     In China, I had English classes five times a week since fifth grade. However, I didn't know how different textbook

English could be from everyday English until I came to Hotchkiss School, Connecticut.

     When I first studied English, I was told to say," I am fine" when people say "How are you?" But in the US, I

found that people say, "I am good" or "I'm tired".

     One day, someone greeted me with "What's up?" It made me confused . I thought for a moment and then smiled

because I didn't know what to say.

Since then, I have discovered more and more differences between Chinese and US cultures.

     To my surprise, US girls spend a lot of time in the burning sun to get a tan(晒黑). However, in China, girls try

every possible way to get their skin paler, or "whiter".

     I was also surprised by how hardworking US students are.  In China, schoolwork is almost everything, so we

study hard and that's it. But here, a "good" student gets good grades, does a lot for the public and plays sports or

music.

     The kids here are so talented, I am starting to be sorry that I gave up playing the piano at an early age and that

I have never thought about sports.

1. What does the word "confused" in the fourth paragraph mean in Chinese ?

A. 困惑

B. 憧憬

C. 悲痛

D. 后悔

2. A good US student spends his / her time ________.

A. only in doing homework

B. on studies, sports or music and public work

C. only in working for the public

D. only on sports or music

3. Which of the following is NOT true?

A. The writer is now in US.

B. American girls love to have white skin.

C. US students are talented and hard working.

D. The writer regrets that he gave up playing the piano.

判断题