搜题请搜索小程序“爱下问搜题”
问题 问答题

(1)设A，曰均为n阶非零矩阵，且A2+A=B2+B=0，证明λ=-1必是矩阵A与B的特征值；
(2)若AB=BA=0，α与β分别是A与B属于特征值λ=-1的特征向量，证明向量组α，β线性无关．

答案

参考答案：(1)因为(E+A)A=0，A≠0，知齐次方程组(E+A)x=0有非零解，即行列式|E+A|=0，所以λ=-1必是矩阵A的特征值．同理λ=-1也必是矩阵B的特征值．
类似地，由AB=0，B≠0，知行列式|A|=0，所以λ=0必是矩阵A的特征值，同理λ=0也必是矩阵B的特征值．
(2)对于Aα=-α，用矩阵B左乘等式的两端有曰BAα=-Bα，又因BA=0，故
Bα=0=0α．
即α是矩阵B属于特征值λ=0的特征向量．
那么，α与β是矩阵β的不同特征值的特征向量，因而α，β线性无关．

单项选择题

People are indulging in an illusion whenever they find themselves explaining at a cocktail (鸡尾酒) party, say, that they are "in computers," or "in telecommunications," or "in electronic funds transfer". The implication is that they are part of the high-tech world. Just between US, they usually aren’t. The researchers who made fundamental breakthroughs in those areas are in a high-tech business. The rest of us are (71) of their work. We use computers and other new technology components to develop our products or to organize our affairs. Because we go about this work in teams and projects and other tightly knit working groups(紧密联系在一起的工作小组), we are mostly in the human communication business. Our successes stem from good human interactions by all participants in the effort, and our failures stem from poor human interactions.

The main reason we tend to focus on the (72) rather than the human side of the work is not because it’s more (73) , but because it’s easier to do. Getting the new disk drive installed is positively trivial compared to figuring out why Horace is in a blue funk (恐惧) or why Susan is dissatisfied with the company after only a few months. Human interactions are complicated and never very crisp (干脆的, 干净利落的) and clean in their effects, but they matter more than any other aspect of the work.

If you find yourself concentrating on the (74) rather than the (75) , you’re like the vaudeville character (杂耍人物) who loses his keys on a dark street and looks for them on the adjacent street because, as he explains, "The light is better there!".

（75）处应填（）。

A．technology

B．sociology

C．physiology

D．astronomy
查看答案
写作题

写作。

请根据你个人对中国的电影的喜好，并且以"I like Chinese movies"为题写一篇作文。

    _________________________________________________________________

____________________________________________________________________

____________________________________________________________________
查看答案