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问题 问答题

已知2维非零向量α不是2阶方阵A的特征向量．

若α，A满足A2α+Aα-6α=0，求A的全部特征值，并由此判定A能否与对角矩阵相似．若能，请写出一个这样的对角矩阵．

答案

参考答案：由题设有
0=A2α+Aα-6α=(A2+A-6E)α
由(Ⅰ)α，Aα线性无关可推出(A-2E)α=Aα-2α≠0．
由(A+3E)[(A-2E)α]=0可推出A+3E有一个特征值为0，从而A有一个特征值为-3．
由(A-2E)[(A+3E)α]=0可推出A-2E有一个特征值为0，从而A有一个特征值为2．
这样A有2个相异的特征值，所以A能与对角矩阵[*]相似．

选择题

在3月5日的学雷锋活动中，某化学兴趣小组为市民检测主要交通路口的空气污染的情况，发现一氧化碳气体的含量超过了国家规定的标准，你认为发生上述情况的主要原因是（　　）

A．人流量太大

B．商店较集中

C．机动车辆排放大量废气

D．生活污水的大量排放
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单项选择题

Starting with his review of Skinner’s Verbal Behavior, Noam Chomsky had led the psycholinguists who argue that man has developed an innate (天生的) capacity for dealing with the linguistic universals common to all languages. Experience and learning then provide only information about the (1) instances of those universal aspects of language which are needed to communicate with other people within a particular language (2) .

This linguistic approach (3) the view that language is built upon learned associations between words. What is learned is not strings of words per se (本身), but (4) rules that enable a speaker to (5) an infinite variety of novel sentences. (6) single words are learned as concepts: they do not stand in a one-to-one (7) with the particular thing signified, but (8) all members of a general class.

This view of the innate aspect of language learning is at first not readily (9) into existing psychological frameworks and (10) a challenge that has stimulated much thought and new research directions. Chomsky argues that a precondition for language development is the existence of certain principles "intrinsic (原有的) to the mind" that provide invariant structures (11) perceiving, learning and thinking. Language (12) all of these processes; thus its study (13) our theories of knowledge in general.

Basic to this model of language is the notion that a child’s learning of language is a kind of theory (14) . It’s thought to be accomplished (15) explicit instruction, (16) of intelligence level, at an early age when he is not capable of other complex (17) or motor achievements, and with relatively little reliable data to go on. (18) , the child constructs a theory of an ideal language which has broad (19) power. Chomsky argues that all children could not develop the same basic theory (20) it not for the innate existence of properties of mental organization which limit the possible properties of languages.

9（）

A.combined

B.integrated

C.blended

D.mixed
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