问题 问答题

已知齐次方程组


同解,求a,b,c.

答案

参考答案:[解法一] 设这两个方程组的系数矩阵分别为A和B,由Ax=0与Bx=0同解,知r(A)=r(B).显然r(B)<3,故|A|=0.于是由
[*]
又由
[*]
得到方程组(Ⅰ)的通解:k(-1,-1,1)T,其中k为任意常数.
把x1=-k,x2=-k,x3=k代入方程组(Ⅱ),得
[*]
当b=1,c=2时,
[*]
方程组(Ⅰ)与(Ⅱ)同解.
当b=0,c=1时,
[*]
由于秩r(A)≠r(B),故此时方程组(Ⅰ)与(Ⅱ)不同解.
因此a=2,b=1,c=2为所求.
[解法二] 因为Ax=0与Bx=0同解[*],而
[*]
因为r(B)<3,那么[*],故
[*]
当b=0,c=1时,r(B)=1而r(A)=2,故应舍去.

阅读理解

阅读理解

     Researchers from the University of Newcastle are leading a worldfirst study which builds on earlier

unpublished research that children are most likely to be guided by their father's eating and exercise habits.

     The new study "Healthy Dads,Healthy Kids",led by Associate Professor Philip Morgan from the

designed to help fathers promote and demonstrate to their children positive behaviours related to physical

activity and healthy eating.

     "The earlier findings showed that children are more likely to follow the example set by their father than

their mother when it comes to eating and exercise," said Morgan.

     Morgan saw striking results in a previous trial involving 165 overweight children.He found children who

lost the most weight had fathers who were engaged in the new eating and exercise plan.

     "We might think mothers are the main influence on children's diet and health,but the reality may be

different," said Morgan. "The roles of fathers are changing.More families have two parents working and

more fathers are involved with food preparation and food shopping than in the past."

     "Fathers influence the food and physical activity habits in the home through their behaviours,attitudes

and approach to food and eating,and act as a role model to their children," said Morgan.

    Researchers are inviting fathers who would like to reduce their weight to join the "Healthy Dads,Healthy

Kids" program.Participation involves attending eight sessions (讲习班) at the University of Newcastle

over six months where the men will receive information,have weightrelated measurements recorded and

complete questionnaires.

     Cooking healthy food with the kids and creating a backyard fitness circuit (循环训练场) are among

the assignments (课外作业) for fathers taking part in the study.

1.What do we learn about the  "Healthy Dads,Healthy Kids" program?

A.It aims to build close family relationships.

B.It involves fathers who want to lose weight.

C.It will last more than eight months.

D.It offers free online courses for parents.

2.Morgan finds a link between children's weight loss and________.

A.their parents' efforts  

B.regular sports training

C.balanced diets  

D.their father's influence

3.According to the earlier research,children seem to ________.

A.copy their father's diets and exercise habits

B.develop healthy eating habits by themselves

C.grow taller if their parents often do exercise

D.help their parents to form exercise habits

4.Which of the following facts causes the change of fathers' roles?

A.That kids have more time to spend with family.

B.That more kids need their father's help in learning.

C.That there are more working mothers than before.

D.That fathers become much busier than before.

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