bài tập ôn tập toán kinh tế giữa kì

Nam
e
:

Clas
s:

Dat
e:

Chapter 03: Matrices

a.

b.

c.

d.

e.

d

ANSWER:
6. Write the transpose of matrix F.

a.

b.

c.

d.

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e.

c

ANSWER:
7. What is the sum of matrix M and its negative?

a.

b.

c.

d.

e.

c

ANSWER:
8. If matrix M has element

, what is ?
a.
b.
c.
d.
e.

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a

ANSWER:
9. Use the following matrices to perform the indicated matrix operations, if possible.

;
a.

b.

c.

d.

e.

e

ANSWER:
10. Use the following matrices to perform the indicated matrix operations, if possible.

;
a.

b.

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c.

d.

e.

e

ANSWER:
11. Use the following matrices to perform the indicated matrix operations, if possible.

;
a.

b.

c.

d.

e.

ANSWER:

b

12. Use the following matrices to perform the indicated matrix operations, if possible.

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;
a.

b.

c.

d.

e.

a

ANSWER:
13. Use the following matrices to perform the indicated matrix operations, if possible.

a.

b.

c.

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d.

e.

c

ANSWER:
14. Use the following matrices to perform the indicated matrix operations, if possible.

;
a.

b.

c.

d.

e.

ANSWER:

d

15. Use the following matrices to perform the indicated matrix operations, if possible.

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;
a.

b.

c.

d.

is undefined
e.
e

ANSWER:
16. Use the following matrices to perform the indicated matrix operations, if possible.

a.

b.

c.

d.

e.

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a

ANSWER:
17. Use the following matrices to perform the indicated matrix operations, if possible.

;
a.

b.

c.

d.

e.

b

ANSWER:
18. Use the following matrices to perform the indicated matrix operations, if possible.

;
a.

b.

c.

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d.

e.

c

ANSWER:
19. Use the following matrices to perform the indicated matrix operations, if possible.

;
a.

b.

c.

d.

e.

c

ANSWER:
20. Find x, y, z and w.

a.

, and

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b.

, and

c.

, and

d.

, and

e.

, and
d

ANSWER:
21. Find x, y, z and w.

a.

and

b.

and

c.

and

d.

and

e.

and
d

ANSWER:
22. Solve for x, y and z.

a.
b.

and
and

c.

and

d.

and

e.

and
a

ANSWER:
23. Find x, y, z, and w .

a.

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and
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b.

and

c.

and

d.

and

e.

and
c

ANSWER:

24. The tables below give the numbers of some species of threatened and endangered wildlife in the United

States and in foreign countries in 2003. Write a matrix A that contains the number of each of these species in
the United States in 2003 and a matrix B that contains the number of each of these species outside the United
States in 2003.

United States
Mammals

Birds

Reptiles

Amphibians

Fish

Amphibians

Fish

Endangered
Threatened
Foreign
Mammals

Birds

Reptiles

Endangered
Threatened
a.

,
b.

,
c.

,
d.

,
e.

,
ANSWER:

d

25. The tables below give the numbers of some species of threatened and endangered wildlife in the United

States and in foreign countries in 2003. Find a matrix with the total number of these species. Assume that
U.S.
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and foreign species are different.
United States

Mammals

Birds

Reptiles

Amphibian
s

Fish

Endangered
Threatened

Foreign
Mammals

Birds

Reptiles

Amphibians

Fish

Endangered
Threatened
a.

b.

c.

d.

e.

b

ANSWER:

26. The tables below give the numbers of some species of threatened and endangered wildlife in the United

States and in foreign countries in 2003. Let A represent the matrix that contains the number of each of these
species in the United States in 2003 and B represent the matrix that contains the number of each of these
species outside the United States in 2003. Find the matrix B – A. What do the negative entries in matrix B – A
mean?
United States
Mammals

Birds

Reptiles

Amphibians

Fish

Amphibians

Fish

Endangered

Threatened
Foreign
Mammals
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Birds

Reptiles

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Endangered
Threatened
a.

The negative entries tell us that that particular species is extinct.
b.

The negative entries tell us how many more endangered or threatened species are in foreign
countries.
c.

The negative entries tell us that there are more endangered or threatened species in foreign countries.
d.

The negative entries tell us that that particular species is extinct.
e.

The negative entries tell us how many more endangered or threatened species are in the United

States.
e

ANSWER:

27. The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their

2002 data. Form a matrix for the 1995 data and a matrix for the 2002 data.
1995
Breed

Rank

Number Registered

Labrador retriever Rottweiler German shepherd Golden
1 retriever Beagle
Poodle
2
Cocker spaniel Dachshund
3
Pomeranian
4
5
6
7
8
9
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Yorkshire terrier

10

2002
Breed
Labrador retriever
Rottweiler

Rank
1
13

German shepherd

3

Golden retriever

2

Beagle
Poodle

4
8

Cocker spaniel
Dachshund

15
5

Pomeranian
Yorkshire terrier

12
6

Number Registered

a.

;
b.

;
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c.

;
d.

;
e.

;
ANSWER:

c

28. The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their

2002 data. Use a matrix operation to find the change from 1995 to 2002 in rank for each breed and in
registration numbers for each breed.

1995


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Breed
Labrador retriever
Rottweiler

Rank
1
2

German shepherd

Golden retriever

3
4

Beagle
Poodle

5
6

Cocker spaniel
Dachshund

7
8

Pomeranian
Yorkshire terrier

9
10

Number Registered

2002
Breed
Labrador retriever
Rottweiler

Rank
1
13

German shepherd

3

Golden retriever

2

Beagle
Poodle

4
8

Cocker spaniel
Dachshund

15
5

Pomeranian
Yorkshire terrier

12
6

Number Registered

a.

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b.

c.

d.

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e.

a

ANSWER:

29. The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their

2002 data. Which breed had the greatest improvement in rank?
1995

Breed
Labrador retriever
Rottweiler

Rank
1
2

German shepherd
Golden retriever

3
4

Beagle
Poodle

5
6

Cocker spaniel
Dachshund

7
8

Pomeranian
Yorkshire terrier

9

10

Number Registered

2002
Breed
Labrador retriever
Rottweiler
German shepherd
Golden retriever
Beagle
Poodle

Rank

Number Registered

Cocker spaniel
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Nam
e
:

Clas
s:

Dat
e:

Chapter 03: Matrices

Dachshund Pomeranian Yorkshire terrier

a.
b.
c.
d.
e.
b

ANSWER:

30. The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their

2002 data. Which breed had the largest increase in the number of registrations?
1995
Breed

Rank

Number Registered

Labrador retriever Rottweiler German shepherd Golden
1 retriever Beagle
Poodle
2

Cocker spaniel Dachshund Pomeranian
3
Yorkshire terrier
4
5
6
7
8
9
10

2002
Breed
Rank
Number Registered
Labrador retriever Rottweiler German shepherd Golden retriever Beagle
Poodle
Cocker spaniel Dachshund

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Pomeranian Yorkshire terrier

a.
b.
c.
d.
e.
e

ANSWER:

31. The following tables give the capital expenditures and gross operating costs of manufacturing establishments

for pollution abatement, in millions of dollars. Use a calculator or spreadsheet to find the sum of the matrices
containing these data. This will yield the total costs of manufacturing establishments for air, water, and solid
contained waste pollution abatement for the years 2002–2005.
Pollution Abatement Capital Expenditures
Air
2002

Water

Solid Contained Waste

Water

Solid Contained Waste

2003
2004
2005
Pollution Abatement Gross Operating Costs

Air
2002
2003
2004
2005
a.

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b.

c.

d.

e.

d

ANSWER:

32. The following tables give the capital expenditures and gross operating costs of manufacturing establishments

for pollution abatement, in millions of dollars. Which type of pollution abatement was most expensive in
2005?
Pollution Abatement Capital Expenditures
Air

2002

Water

Solid Contained Waste

Water

Solid Contained Waste

2003
2004
2005
Pollution Abatement Gross Operating Costs
Air
2002
2003
2004
2005

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a.
b.
c.

Solid Contained Waste

Water
Air
a

ANSWER:

33. The following tables give the death rates, per 100,000 population, by age for selected years for males and

females. If matrix M gives the male data and matrix F gives the female data, use matrix operations to find
the death rate per 100,000 for all people in the age categories given and for the given years.
Males
Under
1

1-4

5-14

15-24

25-34

35-44

45-54

1-4

5-14

15-24

25-34

35-44

45-54

1970
1980
1990
1994
2001
Females
Under
1
1970
1980
1990
1994
2001

a.

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b.

c.

d.

e.

c

ANSWER:

34. The following tables give the death rates, per 100,000 population, by age for selected years for males and

females. If matrix M gives the male data and matrix F gives the female data, find matrix M - F and
describe what it means.
Males
Under
1

1-4

5-14

15-24

25-34

35-44

45-54

1980
1990
1994
2001
Females
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Under
1

1-4

5-14

15-24

25-34

35-44

45-54

1970
1980
1990
1994

2001

a.

M – F represents how much greater the numbers are for males in each category per year.
b.

M – F represents how much greater the numbers are for males in each category per year.
c.

M – F represents how much greater the numbers are for females in each category per year.
d.

M – F represents how much greater the numbers are for females in each category per year.

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