2022 Linear Algebra and Analytic Geometry(Harbin Institute of Technology) 最新满分章节测试答案

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本课程起止时间为:2022-03-15到2022-06-30

【作业】Chapter One Linear Equations in Linear Algebra-Part I Homework 1

1、 问题:This is an augmented matrix of a linear system.Choose h and k such that the system has (a) no solution,(b) a unique solution,(c) many solutions.
评分规则: 【 echelon form right 2 points, each question 2 points.
】

2、 问题:Compute u+v and u-2v,,
评分规则: 【 2 points for each part
】

3、 问题:Let ,, and . For what value(s) of h, y in the plane generated by ?
评分规则: 【 Find the right echelon form, 6 points. ( one point for each nonzero entry ). Find h, 2 points.
】

【作业】Chapter One Linear Equations in Linear Algebra-Part II Homework 2

1、 问题:Write the system first as a vector equation and then as a matrix equation.
评分规则: 【 Vector equationone point for each vector
Matrix Equation2 points for the matrix , one point for the constant vector
】

2、 问题:Write the solution set of the following linear system in parametric vector form.
评分规则: 【 4 points for the reduced echelon form of the augmented matrix2 points for each vector in the paramentric vector form.
】

3、 问题:Find the general flow pattern in the network shown in the figure.
评分规则: 【 3 pint for the system of equations. The form is not unique. 
2 points for the right echelon form. 1 point for the general solution.
】

【作业】Chapter One Linear Equations in Linear Algebra-Part III Howework3

1、 问题:(a)For what value of h is in ? (b) For what value of h is linearly dependent? Justify your answer.
评分规则: 【 1 points for the right augmented matrix. 1 point for the right echelon form. 2 points for the right value of h.
1 points for the right augmented matrix. 1 point for the right echelon form. 2 points for the right value of h.
】

2、 问题:Let ,.Is b in the range of the linear transformation T(x)=Ax? Why or why not?
评分规则: 【 2 points for the right augmented matrix. 2 point for the right echelon form. 2 points for the right conclusion.
】

3、 问题:Let be a linear transformation such that . Find x such that
评分规则: 【 3 pints for the right matrix A. If the matrix is wrong, get 1 point.
2 pints for the right reduced echelon form. 1 point for the right x.
】

Chapter One Linear Equations in Linear Algebra-Part III Test for Chapter 1

1、 问题:Choose the proper value for h and k, such that the system is inconsistent. .
选项：
A:
B:
C:
D:
答案: 【】

2、 问题:Choose the proper value for h and k, such that the system has a unique solution. .
选项：
A:
B:
C:
D:
答案: 【】

3、 问题:Choose the proper value for h and k, such that the system has infinitely many solutions. .
选项：
A:
B:
C:
D:
答案: 【】

4、 问题:Which one of the vector set is linearly independent?
选项：
A:
B:
C:
D:
E:
F:
答案: 【;
】

5、 问题:Choose a matrix A such that the solution set of Ax=0 is a line.
选项：
A:
B:
C:
D:
E:
F:
答案: 【;
;
】

6、 问题:Choose the false statement. There are more than one choices are right.
选项：
A:Every matrix is row equivalent to only one matrix which is in echelon form.
B:A linear system with n equations and n variables has at most n solutions.
C:If a linear system has two different solutions, then it has infinitely many solutions.
D:The system Ax=0 has only the trivial solution if and only if the system has no free variables.
E:If A is an  matrix, the system Ax=b is consistent for all b in , then A has n pivot positions.
F:If A is an  matrix,  and A has n pivot positions, then the system Ax=b is consistent. 
答案: 【Every matrix is row equivalent to only one matrix which is in echelon form.;
A linear system with n equations and n variables has at most n solutions.;
If A is an  matrix, the system Ax=b is consistent for all b in , then A has n pivot positions.】

7、 问题:Choose the true statement. There are more than one choices are right.
选项：
A:If A and B are two row equivalent  matrices, and the columns of A span  , then the columns of B also span .
B: Any vector in S is not a mulptiple of the others, then S is linearly independent.
C:There are 3 linearly independent vectors in . Then n can not be 2.
D:If a set of vectors can span , then there are at least n vectors in the set.
E:There are two vectors u and v in , then .
F:A is a  matrix. T(x)=Ax is a linear transformation from  to .
G:T(x)=Ax is a liear transformation from  to . T is one-to-one if and only if A has a pivot position in every column.
H:T(x)=Ax is a liear transformation from  to . T is onto  if and only if A has a pivot position in every row.
答案: 【If A and B are two row equivalent  matrices, and the columns of A span  , then the columns of B also span .;
There are 3 linearly independent vectors in . Then n can not be 2.;
If a set of vectors can span , then there are at least n vectors in the set.;
There are two vectors u and v in , then .;
T(x)=Ax is a liear transformation from  to . T is one-to-one if and only if A has a pivot position in every column.;
T(x)=Ax is a liear transformation from  to . T is onto  if and only if A has a pivot position in every row.】

8、 问题:. When h=______, the vector b is in .
答案: 【-17】
分析：【The last row of the echelon form is 0 0 h+17. The system is consistent if and only if h+17=0】

9、 问题:When a=_, and  are lineraly dependent?
答案: 【-2】
分析：【a2 is a multiple of a_1, so a=4/(-2)=-2】

【作业】Chapter Two Matrix Algebra Homework for chapter two

1、 问题:Let , Compute 
评分规则: 【 3 points for each answer.
】

2、 问题:Find the inverse of the matrix . Use the inverse to solve the system
评分规则: 【 4 points for the right inverse matrix. 2 points if some entries are wrong.
two pints for x_1, two pints for x_2.
】

3、 问题:Determine the following matrix is invertible or not. Use as feww calculations as possible. Justify your answers.
评分规则: 【 4 points for the judgement. 2 pints for the reason.
】

Chapter Two Matrix Algebra Test for Chapter 2

1、 问题:Which one is C if .
选项：
A:
B:
C:
D:
答案: 【】

2、 问题:Find the value of k such that AB=BA.
选项：
A:k=5
B:k=-5
C:k=3
D:k=-3
答案: 【k=5】

3、 问题:Which of the following matrix is invertible?
选项：
A:
B:
C:
D:
E:
F:
答案: 【;
;
】

4、 问题:T is linear transformation from  to . . Which one is the inverse of T.
选项：
A:
B:
C:
D:
答案: 【】

5、 问题:Which of the discribtion of T is not right. T(x)=Ax, A is an  matrix, m<n.