问题 单项选择题

设α1=(1,2,-1,2)T,α2=(2,0,α,0)T,α3=(1,-2,4,α)T,则α≠3是向量组α1α2α3线性无关的( ).

A.充分而非必要条件

B.必要而非充分条件

C.充分必要条件

D.既非充分也非必要条件

答案

参考答案:A

解析:
此题是判断带有参数的三个向量的线性无关性.只要r(α123)=3,即有α123线性无关.为避免带参数的矩阵消阶梯形求秩,根据题意先设a≠3,如可取a=1(特殊值),则有


得到r(α123)=3,说明a≠3是α123线性无关的充分条件.
再设a=3,得


从而得到r(α123)=3.说明a=3时,α123仍然线性无关,因此a≠3不是α123线性无关的必要条件.
故正确的选择应为A.

阅读理解

第三部分:阅读理解(共20小题;每小题2分,满分40分)

阅读下面短文,从每题所给的四个选项(A、B、C、D)中,选出最佳选项,并在答题卡上将该项涂黑。

We used to go into different chat rooms on different websites . If you wanted to meet someone on the net , you had to go into the same chat room . But now regular net surfers chat on OICQ .

OICQ is an online chat software which is invented by Tencent Computer System Company of Shenzhen in February , 1999 . Since then it has swept the country . Its symbol is a penguin wearing a red scarf .

Net friends can be divided into a buddy list (for good friends ) , a stranger list ( for people you want to avoid on the Net ) . You can also build family lists , co-worker lists , etc .

You can know whether listed friends are online as long as you use it . The cartoon portrait(肖像,画像) of the person turns bright if he is online . And the portrait turns dim(灰暗的) if he is not there .

Traditional public chat rooms are chaotic . It is difficult to focus on a conversation . OICQ can conduct a focused talk without interruptions by other chatters . OICQ has become a regular daily communication tool . “What is your OICQ number ? ” has become a modern topic .

1. OICQ is________.

A. a special chat room for all the cyber citizens(网民)

B. a cartoon portrait to make friends on the Internet

C. an online chat software that helps you talk on the Internet more freely

D. a modern phone number used by more and more people

2. If you don’t want to chat with someone , you can put him in_______with the help of OICQ .

A. a buddy list                   B. a stranger list      

C. family lists                    D. co-worker lists

3. The passage mainly tells us____________.

A. how to chat with people on the Internet

B. how to use OICQ

C. how to choose a regular daily communication tool

D. some advantages about OICQ

单项选择题 B型题