问题 单项选择题

设向量组α1,α2,α3线性无关,向量β1可由α1,α2,α3线性表示,而向量β2不能由α1,α2,α3线性表示.则对任意常数k,必有______.

A.α1,α2,α1,kβ12线性无关

B.α1,α2,α1,kβ12线性相关

C.α1,α2,α1,β1+kβ2线性无关

D.α1,α2,α1,β1+kβ2线性相关

答案

参考答案:A

解析:[考点提示] 线性相关与线性无关.
[解题分析] 由题设,β1可由α1,α2,α3线性表示,则α1,α2,α3,β1线性相关,在C中取k=0,则可看出C不正确.又由β2不能由α1,α2,α3线性表示且α1,α2,α3线性无关,知α1,α2,α3,β2线性无关,在B中取k=0,可看出B不正确.关于A,矩阵(α1,α2,α3,kβ12)可通过初等列变换化为(α1,α2,α3,β2),则该矩阵秩为4,所以α1,α2,α3,kβ12线性无关,所以A正确.关于D,同样可将矩阵(α1,α2,α3,β1+kβ2)化为(α1,α2,α3,kβ2),当k=0时,矩阵的秩为3,则α1,α2,α3,β1+kβ2线性相关.当k≠0时矩阵秩为4,此时α1,α2,α3,β1+kβ2线性无关.所以D不正确.综上,应选A.

阅读理解

Everyone has worries. How do you deal with your worries? There is always something you can do to help yourself feel less worried. Sitting there worrying is no fun and it won’t solve your problems.

Grades at school are often a top worry for kids. ff you worry most about grades, ask yourself these questions:

●  Why are grades important? What do grades mean to me?

●  How do I get ready for class? Do I go over my notes even when there isn’t a test?

●  Do I have a good place to do my homework?

●  Have I tried different ways of studying?

If your worry is about a fight you had with your friend, you might write down al! the things you could do-write a note to him or her, invite him or her to watch a basketball game, say sorry to him or her and so on. Once you have a list of things you could do, you can choose one thing that could get your friend back.

You can ask for help when you’re worried. You can find someone to talk to, such as your parents, friends, and teachers.

小题1:What do kids often worry most about?

A.Their hobbies.

B.Their homework.

C.Their marks at school.

D.A fight with their friends.小题2:According to the passage, when you’re worried, you’d better _______.

A.work hard

B.talk to someone

C.get ready for class

D.write down your worries小题3:If you’re worried about grades, DON’T ask yourself "_______".

A.Why are grades important?

B.What do grades mean to me?

C.How do I get ready for class?

D.Why not give up my studies?小题4:If you had a fight with a friend, you could _______.

A.invite him or her to watch a game

B.put the blame on him or her

C.try to make new friends

D.leave him or her alone小题5:What does the passage mainly tell us?

A.Who is often worried.

B.When people are worried.

C.How to deal with worries.

D.What kinds of worries people have.

单项选择题