问题 单项选择题

设三阶矩阵

,若A的伴随矩阵的秩等于1,则必有
(A) a=b或a+2b=0. (B) a=b或a+2b≠0.
(C) a≠b且a+2b=0. (D) a≠b且a+2b≠0。

答案

参考答案:C

解析: 已知矩阵A而需求是r(A*),故应以r(A*)公式为背景.根据伴随矩阵A*秩的关系式


若a=b,易见r(A)≤1,故可排除(A),(B).
当a≠b时,A中有2阶子式

,若r(A)=2,按定义只需|A|=0.由于


所以应选(C).

阅读理解

阅读理解。

     Scientists are trying to make the deserts into good land again. They want to bring water to the deserts, so

people can live and grow food. They are learning a lot about the deserts. But more and more of the earth is

becoming desert all the time. Scientists may not be able to change the desert in time.

     Why is more and more land becoming desert? Scientists think that people make deserts. People are doing

bad things to the earth.

     Some places on the earth don't get much rain. But they still don't become deserts. This is because some

green plants are growing there. Small green plants and grass are very important to dry places. Plants don't let

the sun make the earth even drier. Plants do not let the wind blow the dirt away. When a bit of rain falls, the

plants hold the water. Without plants, the land can become desert more easily.

1. Deserts _____. [ ]

A. never have any plants or animals in them

B. can all be turned into good land before long

C. are becoming smaller and smaller

D. get very little rain

2. Small green plants are very important to dry places because _____. [ ]

A. they don't let the sun make the earth even drier

B. they don't let the wind blow the soil away

C. they hold water

D. All of the above

3. Land is becoming desert little by little because _____. [ ]

A. plants can't grow there

B. there is not enough rain

C. people haven't done what scientists wish them to do

D. scientists know little about the deserts

4. After reading this passage, we learn that _____. [ ]

A. plants can keep dry land from becoming desert

B. it is good to get rid of the grass in the deserts

C. all places without much rain will become deserts

D. it is better to grow crops on dry land than to cut them

单项选择题