问题 问答题

设A是4阶非零矩阵,α1,α2,α3,α4是非齐次线性方程组Ax=b的不同的解.

如果α1,α2,α3线性相关,证明α12,α13也线性相关;

答案

参考答案:因为α1,α2,α3线性相关,故有不全为0的k1,k2,k3使得k1α1+k2α2+k3α3=0,那么(k1+k2+k31=k212)+k313).
因为α12,α13是齐次方程组Ax=0的解,而α1是非齐次方程组Ax=b的解,所以α1不能由α12,α13线性表出,故必有k1+k2+k3=0.
从而k212)+k313)=0.此时必有k2,k3不全为0(否则k1,k2,k3全为0),即α12,α13线性相关.

单项选择题

Everyone gets angry sometimes, but being angry doesn’t really solve much. Your goal is to calm yourself down. This is (1) for some people. Instead of calming down, they might get more and more upset (2) they explode like a volcano. Some people might say they have trouble (3) their temper. Sometimes angry feelings can be hard to (4) . So what do you do if your temper is like a volcano

Well, the good news is (5) people don’t keep making the same mistakes over and over again. You can train your temper. Here are steps you can (6) at any time.

Get a lot of (7) activity. Exercise can be good because it is a way of (8) energy and stress. You can dance around your room (9) your favorite music, too.

Talk to your mom or dad. If you’re having trouble with your temper, tell your parents you’re trying to do a (10) job of controlling yourself. Let them know you are going to ask for their help.

Put (11) into words. Get into the habit of saying what you are feeling and why. (12) using words might help you manage your p feelings and behaviors.

Take a break from the (13) . If you are in an argument with someone, go to another part of your house. You can just say, "I want to be (14) for a while so I can calm down. "

Go into a (15) . If you fed angry and think you need a timeout to calm down, don’t (16) your parents to tell you to take a timeout for yourself. Let your family know that when you’re taking a timeout, they need to (17) your space and leave you alone. While you are sitting in your chair, try to take deep (18) .

Learn to shift. The idea is to shift from a really angry mood to a better mood. After you (19) the angry feelings out, you have to start thinking about other things, You can say, "I (20) my temper, but I’m going to get myself under control now.

12()

A. Although

B. Since

C. So

D. But

多项选择题