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Chapter 1 l Assignments 1

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Assignment Assignment for Lesson 1.1

Name _____________________________________________ Date ____________________

Arrays, Arrays! Introduction to Matrices and Matrix Operations

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

V � � 1

�1

2

�3

�2

3

� W � � 2

8

0

�4

6

3

5

�1

8

� X � � 6

�4 �10

8

0

�2 �

Y � � 0

�5

1

�4

�11

0

�2

14

�6

� Z � � �4

16

�5

15

�20

9

� a. V � Z

b. W � Y

c. X � X

d. 10Y

e. 2Z � 3V

2 Chapter 1 l Assignments

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f. 1 __ 2

(Y � W )

2. A small candle-making company sells candles of different scents and sizes. The

available sizes are small, medium, and large. The available scents are vanilla ( V ),

pine (P), apple (A), lavender (L), and berry (B). The matrix represents the number of

candles the company sold last month. Use this information to complete parts (a)

through (g).

V P A L B

Small:

Medium:

Large:

� 12

17

14

2

3

1

9

13

8

6

7

7

15

11

10

�

a. What are the dimensions of the matrix?

b. What does the entry a32

represent?

c. How many small berry-scented candles did the company sell last month?

d. What size candle was the most popular last month? How do you know?


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e. What scent of candle was the least popular last month? How do you know?

f. How many total candles did the company sell last month? Explain how you

calculated your answer.

g. The matrix shown represents the number of candles that the company has sold

so far this month. Suppose that the company set a goal this month to sell twice

as many of each size and scent of candle as they did last month. Write a matrix

to show how many more candles the company needs to sell this month to reach

their goal.

V P A L B

Small:

Medium:

Large:

� 22

30

28

4

6

1

13

24

9

10

13

11

15

22

15

�


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Name _____________________________________________ Date ____________________

School Daze Matrix Multiplication

1. Use the following matrices to perform the indicated operations, if possible. If it is

not possible, explain why.

K � � 0

�1 �3

5

� L � � 6

�1 �4

1

3

�2 � M � �

�3

�7

0

�3

1

8

� N � � 2

�5

1

4

1

0

�1

10

�3

� a. KL

b. LK

c. K 2

d. ML


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e. L 2

f. NM

g. K3

h. N2M

i. M T

j. N T


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Name _____________________________________________ Date ____________________

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2. A small family video store rents out new release DVDs and older title DVDs only.

The DVDs are categorized by genre — comedy, drama, action, horror, or other.

• Of the 500 comedy DVDs in the store, 100 are new releases.

• Of the 450 drama DVDs in the store, 100 are new releases.

• Of the 350 action DVDs in the store, 100 are new releases.

• Of the 200 horror DVDs in the store, 50 are new releases.

• Of the 250 other DVDs in the store, 50 are new releases.

• During an average month, 10% of the new releases and 8% of the older title

DVDs are returned late.

• Each year, about 12% of the new releases and 20% of the older title DVDs

are damaged.

a. Write a 2 � 2 matrix P to represent the percentage of new release and older title

DVDs that are returned late and the percentage of new release and older title DVDs

that are damaged. Let the columns represent new release and older title DVDs. Let

the rows represent the DVDs that are returned late and the DVDs that are damaged.

b. Write a 2 � 5 matrix G to represent the number of new release and older title

DVDs in each genre. Let the columns represent the genre and let the rows

represent new release DVDs and older title DVDs.

c. Calculate the product PG and explain what the product matrix means in terms

of the problem situation.


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d. About how many action DVDs are damaged each year?

e. About how many comedy DVDs are returned late each month?


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Name _____________________________________________ Date ____________________

Commune, Associate? Properties of Matrix Operations

1. Consider the matrix M � � �4

3

2

�4 � .

a. What is the additive identity matrix I?

b. What is the additive inverse matrix N?

c. What is the multiplicative identity matrix I?

2. Use matrices J and K to complete parts (a) through (c).

J � � 9

�3 �6

�5

4

�7 � K � �

6

�4

5

0

�3

1

� a. Calculate JK, if possible. If it is not possible, explain why.

b. Calculate KJ, if possible. If it is not possible, explain why.

c. Complete the following statement with � or �: JK KJ.


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3. Use matrices V, W, and X to complete parts (a) through (c).

V � [10 �5 �12] W � [�4 0 15] X � [8 7 1]

a. Calculate V � (W � X), if possible. If it is not possible, explain why.

b. Calculate (V � W) � X, if possible. If it is not possible, explain why.

c. Complete the following statement with � or �: V � (W � X) (V � W) � X.

4. Use matrices F, G, and H to complete parts (a) through (c).

F � � �2

�2 �1

0

� G � � 3

�2 �2

5

1

�1 � H � � 0

3

1

�2

3

2 �

a. Calculate F(G � H), if possible. If it is not possible, explain why.

b. Calculate FG � FH, if possible. If it is not possible, explain why.

c. Complete the following statement with � or �: F(G � H ) FG � FH.


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5. Use matrices S and T to complete parts (a) through (c).

S � � �1

0

3

�4 � T � � 2

3 �2

1 �

a. Calculate (S � T )2, if possible. If it is not possible, explain why.

b. Calculate S2 � 2ST � T 2, if possible. If it is not possible, explain why.

c. Complete the following statement with � or �: (S � T)2 S2 � 2ST � T 2.


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Name _____________________________________________ Date ____________________

Inverses, Anyone? Row Operations and Multiplicative Inverses

Solve the system of linear equations using Gaussian elimination. Describe each step. Then check your solution.

1. � 2x � 6y � 18

x � 5y � �15

2. � 3x � 2y � 4

�5x � 6y � �4


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3. � �x � y � 3

4x � 7y � �6

Determine the multiplicative inverse of matrix A by transforming the equation AA�1 � I into the equation IA�1 � A�1 using elementary row operations. Describe each step. Then check your answer.

4. A � � 5 3

4

2 �


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5. B � � 0

�1

2

�6 �

6. C � � 5

1.5

3

1 �


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Use a graphing calculator to determine the multiplicative inverse of the matrix.

7. C � � 3

�1 �5

2 � 8. Z � � �2

1

5

�8 �

Let matrix A be represented by A � � a c b d

� . Use the fact that

A�1 � 1 ________ ad � bc

� d �c �b a � to determine the inverse of the given matrix.

Show your work.

9. A � � 10

�5

4

�3 � 10. A � � �3

6

5

�2 �


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Name _____________________________________________ Date ____________________

Solutions Abound! Matrix Equations

Write each system of linear equations as a matrix equation. Then use a calculator to determine the inverse of the matrix, and use the inverse to solve the system of equations. Then check your solutions.

1. � 3x � 5y � 7

�x � 2y � �1 2. � �5x � 4y � �14

3x � y � �7


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3.

� 4x � 5y � 3z � 5

�2x � 7y � z � �1

x � 3y � 2z � 6

4. � 2x � 4y � 3z � 0

�x � 5y � 2z � 7

�5x � 2y � 3z � �3

5. Use a matrix equation to determine the equation of a line that passes through the points

(�3, �13) and (6, 2). Check your answer.


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6. Use a matrix equation to determine the equation of a parabola that passes through the

points (�2, �13), (1, 6.5), and (4, 17).


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Name _____________________________________________ Date ____________________

Determining Determinants! Determinants

Use Cramer’s Rule to solve each system of equations. Check your solution.

1. � 2x � 5y � 0

�3x � 8y � 2

2. � 2.2x � 0.5y � �5

�3.8x � 1.6y � �0.2


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4. Use determinants to calculate the area of the triangle shown.

x43

1

3

4

–1–1

21–2

–2

–3

–3

–4

–4

y

2

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