问题 填空题

设A是2阶矩阵,非齐次线性方程组AX=b有通解X=k(-2,1)T+(3,-4)T(k为任意常数),b=(3,2)T又设β(5,-10)T,则Aβ=______。

答案

参考答案:(9,6)T

解析:[考点] 任一2维向量由线性非齐次方程组的解与其导出组的解线性表示
[答案解析] 记ξ=(-2,1)T,η=(3,-4)T,则ξ,η线性无关,且Aξ=0,Aη=b
令β=x1ξ+x2η,则
[*]
即[*]
于是Aβ=A(2ξ+3η)=2Aξ+3Aη=0+3(3,2)T=(9,6)T

阅读理解

Li Denghai, with his muddy boots and tanned(晒黑的) face, may not look like he is one of China’s famous agricultural pioneers. But the 61-year-old man from Shandong Province has made scientific breakthroughs(突破), which made great contributions to China’s food security(安全). His main work has been in achieving the higher output of corn production.

Li, who holds the world record for the highest output of summer corn, once says, “Corn has a life; it sings and dances. If you listen clearly, it can speak to you.” He started his research in 1969 when he was 20 and just dropped out of a high school. He then read an article which pointed that corn output per mu in the USA was six times higher than that in China. He was shocked and set out to work on just a small piece of land round the clock to see if he could increase the output. He often went to the field with a flashlight late at night, if he had been away during the day. By careful nurturing (照料) he managed to double the output.

Li Denghai was awarded the “China Award for Significant Contribution to the Maize (玉米) Industry” in 2005, and the same year the company named after his own name came into the market on the Shenzhen Stock Exchange. Li, however, is never happier than when he is in the middle of his cornfields. “I can forget my tiredness when talking to my corns,” he says.

小题1:When Li Denghai began the study of corn,       .

A.he just graduated from an ordinary high school

B.he was shocked that the corn output in China was so low

C.he was only in his thirties

D.he wasn’t really fond of his work小题2:The underlined phrase “round the clock” means     .

A.day and night

B.sooner or later

C.face to face

D.now and then小题3:From Mr. Li’s words in this passage, we can learn that     .

A.he is not good at communicating with people

B.he is too tired to go to the corn fields

C.he talks to his corn when feeling lonely

D.he loves his career deeply

单项选择题