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Determine whether each matrix product is
defined. If so, state the dimensions of the
product.
1.
ANSWER:
2×3
2.
ANSWER:
undefined
3.
ANSWER:
8×10
Find each product, if possible.
4.
ANSWER:
5.
ANSWER:
6.
ANSWER:
7.
ANSWER:
3-6 Multiplying Matrices
Determine whether each matrix product is
defined. If so, state the dimensions of the 8.
product.
1.
ANSWER:
Undefined
ANSWER:
2×3
9.
2.
ANSWER:
ANSWER:
undefined
3.
10.
ANSWER:
8×10
Find each product, if possible. ANSWER:
4.
ANSWER:
11.
5.
ANSWER:
ANSWER:
12. CCSS SENSE-MAKINGThe table shows the
number of people registered for aerobics for the first
quarter.
6. Quinn’s Gym charges the following registration fees:
class-by-class, $165; 11-class pass, $110; unlimited
pass, $239.
ANSWER:
7.
ANSWER:
a. Write a matrix for the registration fees and a
matrix for the number of students.
b. Find the total amount of money the gym received
from aerobics and step aerobic registrations.
8.
eSolutions Manual - Powered by Cognero ANSWER: Page1
ANSWER: a.
Undefined
b
. $22,955
9.
Use to
ANSWER:
determine whether the following equations are
true for the given matrices.
13. XY = YX
ANSWER:
10.
No;
ANSWER:
14. X(YZ) = (XY)Z
ANSWER:
Yes; and
11.
ANSWER: Determine whether each matrix product is
defined. If so, state the dimensions of the
product.
15. P · Q
12. CCSS SENSE-MAKINGThe table shows the 2 × 3 3 × 4
number of people registered for aerobics for the first
quarter. ANSWER:
Quinn’s Gym charges the following registration fees: 2×4
class-by-class, $165; 11-class pass, $110; unlimited
pass, $239. 16. A · B
5 × 5 5 × 5
ANSWER:
5×5
17. M3 × 1 · N2 × 3
a. ANSWER:
Write a matrix for the registration fees and a undefined
matrix for the number of students.
b. Find the total amount of money the gym received 18. X · Y
from aerobics and step aerobic registrations. 2 × 6 6 × 3
ANSWER:
ANSWER:
2×3
a. 19. J · K
2 × 1 2 × 1
b ANSWER:
. $22,955 undefined
Use to 20. S · T
5 × 2 2 × 4
determine whether the following equations are
ANSWER:
true for the given matrices.
5×4
13. XY = YX Find each product, if possible.
ANSWER:
21.
No;
ANSWER:
[ 26 ]
14. X(YZ) = (XY)Z
ANSWER:
22.
Yes; and
ANSWER:
Determine whether each matrix product is
defined. If so, state the dimensions of the
23.
product.
15. P · Q ANSWER:
2 × 3 3 × 4
ANSWER:
2×4
24.
16. A · B
5 × 5 5 × 5
ANSWER:
ANSWER:
5×5
17. M3 × 1 · N2 × 3
25.
ANSWER:
undefined
18. X · Y ANSWER:
2 × 6 6 × 3 Undefined
ANSWER:
2×3
26.
19. J · K
2 × 1 2 × 1
ANSWER:
ANSWER:
undefined
20. S · T
5 × 2 2 × 4
ANSWER:
27.
5×4
Find each product, if possible.
ANSWER:
21.
ANSWER:
[ 26 ]
28.
22.
ANSWER:
ANSWER:
TRAVEL The Wolf family owns three bed and
29.
breakfasts in a vacation spot. A room with a single
bed is $220 a night, a room with two beds is $250 a
night, and a suite is $360.
23.
ANSWER:
24.
a. Write a matrix for the number of each type of
ANSWER: room at each bed and breakfast. Then write a room-
cost matrix.
b. Write a matrix for total daily income, assuming
that all the rooms are rented.
c. What is the total daily income from all three bed
and breakfasts, assuming that all the rooms are
25. rented?
ANSWER: ANSWER:
Undefined
a.
26.
b.
ANSWER:
c.
$5060
Use , and k
= 2 to determine whether the following
27.
equations are true for the given matrices.
30. k(PQ) = P(kQ)
ANSWER:
ANSWER:
Yes;
28.
31. PQR = RQP
ANSWER:
ANSWER:
No;
TRAVEL The Wolf family owns three bed and 32. PR + QR = (P + Q)R
29.
breakfasts in a vacation spot. A room with a single
bed is $220 a night, a room with two beds is $250 a ANSWER:
night, and a suite is $360. Yes;
33. R(P + Q) = PR + QR
ANSWER:
No;
CCSS SENSE-MAKINGStudent Council is selling
34.
a. Write a matrix for the number of each type of flowers for Mother’s Day. They bought 200 roses,
room at each bed and breakfast. Then write a room- 150 daffodils, and 100 orchids for the purchase prices
cost matrix. shown. They sold all of the flowers for the sales
b. Write a matrix for total daily income, assuming prices shown.
that all the rooms are rented.
c. What is the total daily income from all three bed
and breakfasts, assuming that all the rooms are
rented?
ANSWER:
a.
a. Organize the data in two matrices, and use matrix
multiplication to find the total amount that was spent
on the flowers.
b. b. Write two matrices, and use matrix multiplication
to find the total amount the student council received
c. for the flower sale.
$5060
c. Use matrix operations to find how much money
the student council made on their project.
Use , and k
ANSWER:
= 2 to determine whether the following a. $747.50
equations are true for the given matrices. b. $1387.50
c. $640
30. k(PQ) = P(kQ)
AUTO SALESA car lot has four sales associates.
35.
ANSWER: At the end of the year, each sales associate gets a
Yes; bonus of $1000 for every new car they have sold and
$500 for every used car they have sold.
31. PQR = RQP
ANSWER:
No;
32. PR + QR = (P + Q)R
ANSWER:
Yes; a. Use a matrix to determine which sales associate
earned the most money.
b. What is the total amount of money the car lot
spent on bonuses for the sales associates this year?
33. R(P + Q) = PR + QR
ANSWER:
ANSWER:
No;
a.
CCSS SENSE-MAKINGStudent Council is selling
34.
flowers for Mother’s Day. They bought 200 roses,
150 daffodils, and 100 orchids for the purchase prices b. $187,500
shown. They sold all of the flowers for the sales
prices shown. Use matrices
to find
each of the following. If the matrix does not
exist, write undefined.
XY
36.
ANSWER:
undefined
a. Organize the data in two matrices, and use matrix
multiplication to find the total amount that was spent
on the flowers. 37. YX
b. Write two matrices, and use matrix multiplication
to find the total amount the student council received ANSWER:
for the flower sale.
c. Use matrix operations to find how much money
the student council made on their project.
ANSWER: ZY
a. $747.50 38.
b. $1387.50 ANSWER:
undefined
c. $640
39. YZ
AUTO SALESA car lot has four sales associates.
35.
At the end of the year, each sales associate gets a
bonus of $1000 for every new car they have sold and ANSWER:
$500 for every used car they have sold.
40. (YX)Z
ANSWER:
a. Use a matrix to determine which sales associate (XZ)X
earned the most money. 41.
b. What is the total amount of money the car lot
spent on bonuses for the sales associates this year? ANSWER:
undefined
ANSWER: X(ZZ)
42.
ANSWER:
a. undefined
43. (XX)Z
b. $187,500
ANSWER:
Use matrices
to find
CAMERASPrices of digital cameras depend on
each of the following. If the matrix does not 44.
features like optical zoom, digital zoom, and
exist, write undefined. megapixels.
XY
36.
ANSWER:
undefined
37. YX
ANSWER: a. The 10-mp cameras are on sale for 20% off, and
the other models are 10% off. Write a new matrix
for these changes.
b. Write a new matrix allowing for a 6.25% sales tax
on the discounted prices.
ZY c. Describe what the differences in these two
38.
matrices represent.
ANSWER:
undefined ANSWER:
39. YZ a.
ANSWER:
b.
40. (YX)Z
ANSWER:
c. sales tax
BUSINESSThe Kangy Studio has packages
45.
available for senior portraits.
41. (XZ)X
ANSWER:
undefined
X(ZZ)
42.
ANSWER:
undefined
(XX)Z
43.
a. Use matrices to determine the total cost of each
ANSWER:
package.
b. The studio offers an early bird discount of 15% off
any package. Find the early bird price for each
package.
CAMERASPrices of digital cameras depend on
44.
features like optical zoom, digital zoom, and ANSWER:
megapixels. a. A: $421; B: $274; C: $150; D: $68
b. A: $357.85; B: $232.90; C: $127.50; D: $57.80
REASONING AB has
46. If the product matrix
A
dimensions 5 × 8, and has dimensions 5 × 6, what
are the dimensions of matrix B?
ANSWER:
a. The 10-mp cameras are on sale for 20% off, and 6 × 8
the other models are 10% off. Write a new matrix
CCSS ARGUMENTSShow that each property of
47.
for these changes. matrices.
b. Write a new matrix allowing for a 6.25% sales tax a. Scalar Distributive Property
on the discounted prices. b. Matrix Distributive Property
c. Describe what the differences in these two
matrices represent. c. Associative Property of Multiplication
d. Associative Property of Scalar Multiplication
ANSWER:
ANSWER:
a.
a.
b.
c. sales tax
BUSINESSThe Kangy Studio has packages
45.
available for senior portraits. b.
a. Use matrices to determine the total cost of each
package.
b. The studio offers an early bird discount of 15% off
any package. Find the early bird price for each
package.
ANSWER:
a. A: $421; B: $274; C: $150; D: $68
b. A: $357.85; B: $232.90; C: $127.50; D: $57.80
REASONING AB has c.
46. If the product matrix
A
dimensions 5 × 8, and has dimensions 5 × 6, what
are the dimensions of matrix B?
ANSWER:
6 × 8
CCSS ARGUMENTSShow that each property of
47.
matrices.
a. Scalar Distributive Property
b. Matrix Distributive Property
c. Associative Property of Multiplication
d. Associative Property of Scalar Multiplication
d.
ANSWER: Substi
a.
c(AB) =
Defini
c
=
Defini
=
Distri
=
Defini
b.
=
Defini
= (cA)B Substi
Subst
c(AB) =
Defini
= c
Defini
=
Distri
=
Com
=
Defini
c. =
= A(cB) Substi
OPEN ENDEDWrite two matrices A and B such
48.
that AB = BA.
ANSWER:
Sample Answer:
CHALLENGE
49. Find the missing values in
d.
Substi
c(AB) =
Defini ANSWER:
a = 2, b = 1, c = 3, d = 4
c
=
WRITING IN MATHUse the data on Lisa Leslie
Defini 50.
found at the beginning of the lesson to explain how
= matrices can be used in sports statistics. Describe a
Distri matrix that represents the total number of points she
has scored during her career and an example of a
= sport in which different point values are used in
Defini scoring.
=
Defini ANSWER:
Sports statistics are often listed in columns and
matrices. In this case, you can find the total number
= (cA)B Substi of points scored by multiplying the point value matrix,
which does not change, by the scoring matrix, which
changes after each season. The total number of
Subst points for her career can be found by multiplying the
c(AB) = scoring matrix S by the point matrix P. Basketball
Defini and wrestling use different point values in scoring.
GRIDDED RESPONSEThe average (arithmetic
= c 51.
Defini mean) of r, w, x, and y is 8, and the average of x and
y is 4. What is the average of r and w?
=
Distri ANSWER:
12
= Carla, Meiko, and Kayla went shopping to get ready
Com 52.
for college. Their purchases and total amounts spent
are shown in the table below.
=
Defini
=
= A(cB) Substi
Assume that all of the shirts were the same price, all
OPEN ENDEDWrite two matrices A and B such
48. of the pants were the same price, and all of the shoes
that AB = BA. were the same price. What was the price of each
item?
ANSWER:
A
shirt, $12.95; pants, $15.99; shoes, $23.49
Sample Answer: B
shirt, $15.99; pants, $12.95; shoes, $23.49
C
shirt, $15.99; pants, $23.49; shoes, $12.95
D
CHALLENGE shirt, $23.49; pants, $15.99; shoes, $12.95
49. Find the missing values in
ANSWER:
A
GEOMETRY Rectangle LMNQ has diagonals that
53.
ANSWER: intersect at point P. Which of the following
a = 2, b = 1, c = 3, d = 4 represents point P?
WRITING IN MATHUse the data on Lisa Leslie
50.
found at the beginning of the lesson to explain how
matrices can be used in sports statistics. Describe a
matrix that represents the total number of points she
has scored during her career and an example of a
sport in which different point values are used in F
scoring. (2, 2)
G
(1, 1)
H
(0, 0)
J 1, 1)
ANSWER: (− −
Sports statistics are often listed in columns and
matrices. In this case, you can find the total number ANSWER:
of points scored by multiplying the point value matrix, H
which does not change, by the scoring matrix, which SAT/ACT What are the dimensions of the matrix
changes after each season. The total number of 54.
points for her career can be found by multiplying the that results from the multiplication shown?
scoring matrix S by the point matrix P. Basketball
and wrestling use different point values in scoring.
GRIDDED RESPONSEThe average (arithmetic
51.
mean) of r, w, x, and y is 8, and the average of x and A
y is 4. What is the average of r and w? 1 × 4
B
3 × 3
ANSWER: C
12 3 × 1
D
4 × 1
E
Carla, Meiko, and Kayla went shopping to get ready 4 × 3
52.
for college. Their purchases and total amounts spent
are shown in the table below. ANSWER:
D
Perform the indicated operations. If the matrix
does not exist, write impossible.
55.
Assume that all of the shirts were the same price, all ANSWER:
of the pants were the same price, and all of the shoes
were the same price. What was the price of each
item?
A
shirt, $12.95; pants, $15.99; shoes, $23.49
B
shirt, $15.99; pants, $12.95; shoes, $23.49
C 56.
shirt, $15.99; pants, $23.49; shoes, $12.95
D
shirt, $23.49; pants, $15.99; shoes, $12.95
ANSWER:
ANSWER:
A
GEOMETRY Rectangle LMNQ has diagonals that
53.
intersect at point P. Which of the following
represents point P? 57.
ANSWER:
F Solve each system of equations.
(2, 2)
G
(1, 1)
H
(0, 0)
J 1, 1)
(− −
58.
ANSWER:
H ANSWER:
(–2, 5, 7)
SAT/ACT What are the dimensions of the matrix
54.
that results from the multiplication shown?
59.
ANSWER:
(8, 3, 1)
A
1 × 4
B
3 × 3
C
3 × 1
D
4 × 1
60.
E
4 × 3
ANSWER:
ANSWER: ( 3, 2, 6)
D – –
MEDICINEThe graph shows how much
Perform the indicated operations. If the matrix 61.
Americans spent on doctors visits in some recent
does not exist, write impossible. ’
years and a prediction for 2014.
a. Find a regression equation for the data without the
55. predicted value.
b. Use your equation to predict the expenditures for
ANSWER: 2014.
c. Compare your prediction to the one given in the
graph.
56.
ANSWER:
57.
ANSWER:
a.
ANSWER: Sample answer: y = 116.25x - 231,176.97
b. Sample answer: $2950.53 billion
c. The value predicted by the equation is significantly
lower than the one given in the graph.
Solve each system of equations. How many different ways can the letters of the word
62.
MATHEMATICS be arranged?
ANSWER:
58. 4,989,600
ANSWER: Describe the transformation in each function.
(–2, 5, 7) Then graph the function.
63.
ANSWER:
Translated 4 units to the right and 3 units up.
59.
ANSWER:
(8, 3, 1)
60.
ANSWER:
(–3, 2, –6)
MEDICINEThe graph shows how much
61.
Americans spent on doctors visits in some recent 64.
’
years and a prediction for 2014.
a. Find a regression equation for the data without the ANSWER:
predicted value. Translated 3 units to the left and 5 units down and
b. Use your equation to predict the expenditures for stretched vertically..
2014.
c. Compare your prediction to the one given in the
graph.
65.
ANSWER:
Translated 2 units to the left and 6 units down.
ANSWER:
a. Sample answer: y = 116.25x - 231,176.97
b. Sample answer: $2950.53 billion
c. The value predicted by the equation is significantly
lower than the one given in the graph.
62. How many different ways can the letters of the word
MATHEMATICS be arranged?
ANSWER:
4,989,600
Describe the transformation in each function.
Then graph the function.
63.
ANSWER:
Translated 4 units to the right and 3 units up.
64.
ANSWER:
Translated 3 units to the left and 5 units down and
stretched vertically..
65.
ANSWER:
Translated 2 units to the left and 6 units down.
Determine whether each matrix product is
defined. If so, state the dimensions of the
product.
1.
ANSWER:
2×3
2.
ANSWER:
undefined
3.
ANSWER:
8×10
Find each product, if possible.
4.
ANSWER:
5.
ANSWER:
6.
ANSWER:
7.
ANSWER:
Determine whether each matrix product is
defined. If so, state the dimensions of the
product.
1.
ANSWER: 8.
2×3
ANSWER:
Undefined
2.
ANSWER:
undefined 9.
ANSWER:
3.
ANSWER:
8×10
Find each product, if possible.
10.
4.
ANSWER:
ANSWER:
5.
11.
ANSWER:
ANSWER:
6.
12. CCSS SENSE-MAKINGThe table shows the
number of people registered for aerobics for the first
ANSWER: quarter.
Quinn’s Gym charges the following registration fees:
class-by-class, $165; 11-class pass, $110; unlimited
pass, $239.
7.
ANSWER:
8. a. Write a matrix for the registration fees and a
matrix for the number of students.
b. Find the total amount of money the gym received
ANSWER: from aerobics and step aerobic registrations.
Undefined
ANSWER:
9.
a.
ANSWER:
b
. $22,955
Use to
determine whether the following equations are
10.
true for the given matrices.
13. XY = YX
ANSWER:
ANSWER:
No;
14. X(YZ) = (XY)Z
11.
ANSWER:
Yes; and
ANSWER:
3-6 Multiplying Matrices
Determine whether each matrix product is
12. CCSS SENSE-MAKINGThe table shows the
number of people registered for aerobics for the first defined. If so, state the dimensions of the
quarter. product.
Quinn’s Gym charges the following registration fees:
class-by-class, $165; 11-class pass, $110; unlimited 15. P · Q
pass, $239. 2 × 3 3 × 4
ANSWER:
2×4
16. A · B
5 × 5 5 × 5
ANSWER:
a. Write a matrix for the registration fees and a 5×5
matrix for the number of students.
b. Find the total amount of money the gym received 17. M3 × 1 · N2 × 3
from aerobics and step aerobic registrations.
ANSWER:
undefined
ANSWER:
18. X · Y
a. 2 × 6 6 × 3
ANSWER:
b 2×3
. $22,955
19. J · K
Use to 2 × 1 2 × 1
determine whether the following equations are ANSWER:
undefined
true for the given matrices.
20. S · T
5 × 2 2 × 4
13. XY = YX
ANSWER:
ANSWER:
No; 5×4
Find each product, if possible.
21.
14. X(YZ) = (XY)Z
ANSWER:
ANSWER:
Yes; and [ 26 ]
22.
Determine whether each matrix product is ANSWER:
defined. If so, state the dimensions of the
product.
15. P · Q
2 × 3 3 × 4
23.
ANSWER:
eSolutions Manual - Powered by Cognero Page2
2×4
ANSWER:
16. A · B
5 × 5 5 × 5
ANSWER:
5×5
24.
17. M3 × 1 · N2 × 3
ANSWER:
ANSWER:
undefined
18. X · Y
2 × 6 6 × 3
25.
ANSWER:
2×3
ANSWER:
19. J · K Undefined
2 × 1 2 × 1
ANSWER:
undefined 26.
20. S · T
5 × 2 2 × 4
ANSWER:
ANSWER:
5×4
Find each product, if possible.
21.
27.
ANSWER:
[ 26 ] ANSWER:
22.
28.
ANSWER:
ANSWER:
23.
TRAVEL The Wolf family owns three bed and
29.
breakfasts in a vacation spot. A room with a single
ANSWER: bed is $220 a night, a room with two beds is $250 a
night, and a suite is $360.
24.
ANSWER:
a. Write a matrix for the number of each type of
room at each bed and breakfast. Then write a room-
cost matrix.
25. b.
Write a matrix for total daily income, assuming
that all the rooms are rented.
ANSWER:
Undefined c. What is the total daily income from all three bed
and breakfasts, assuming that all the rooms are
rented?
ANSWER:
26.
a.
ANSWER:
b.
c.
$5060
27.
Use , and k
ANSWER:
= 2 to determine whether the following
equations are true for the given matrices.
30. k(PQ) = P(kQ)
28.
ANSWER:
Yes;
ANSWER:
31. PQR = RQP
TRAVEL The Wolf family owns three bed and ANSWER:
29.
breakfasts in a vacation spot. A room with a single No;
bed is $220 a night, a room with two beds is $250 a
night, and a suite is $360.
PR+QR=(P+Q)R
32.
ANSWER:
Yes;
33. R(P + Q) = PR + QR
a. Write a matrix for the number of each type of ANSWER:
room at each bed and breakfast. Then write a room- No;
cost matrix.
b.
Write a matrix for total daily income, assuming CCSS SENSE-MAKINGStudent Council is selling
34.
that all the rooms are rented. flowers for Mother s Day. They bought 200 roses,
’
c. What is the total daily income from all three bed 150 daffodils, and 100 orchids for the purchase prices
and breakfasts, assuming that all the rooms are shown. They sold all of the flowers for the sales
rented? prices shown.
ANSWER:
a.
b.
a. Organize the data in two matrices, and use matrix
c. multiplication to find the total amount that was spent
$5060 on the flowers.
Use , and k b. Write two matrices, and use matrix multiplication
to find the total amount the student council received
= 2 to determine whether the following for the flower sale.
c. Use matrix operations to find how much money
equations are true for the given matrices. the student council made on their project.
ANSWER:
30. k(PQ) = P(kQ)
a. $747.50
ANSWER: b. $1387.50
Yes;
c. $640
AUTO SALESA car lot has four sales associates.
35.
At the end of the year, each sales associate gets a
31. PQR = RQP bonus of $1000 for every new car they have sold and
ANSWER: $500 for every used car they have sold.
No;
32. PR + QR = (P + Q)R
ANSWER:
Yes;
33. R(P + Q) = PR + QR
a. Use a matrix to determine which sales associate
ANSWER: earned the most money.
No; b. What is the total amount of money the car lot
spent on bonuses for the sales associates this year?
CCSS SENSE-MAKINGStudent Council is selling
34.
flowers for Mother s Day. They bought 200 roses, ANSWER:
’
150 daffodils, and 100 orchids for the purchase prices
shown. They sold all of the flowers for the sales a.
prices shown.
b. $187,500
Use matrices
to find
each of the following. If the matrix does not
a. Organize the data in two matrices, and use matrix exist, write undefined.
XY
multiplication to find the total amount that was spent 36.
on the flowers.
b. Write two matrices, and use matrix multiplication ANSWER:
to find the total amount the student council received undefined
for the flower sale.
37. YX
c. Use matrix operations to find how much money
the student council made on their project.
ANSWER:
ANSWER:
a. $747.50
b. $1387.50
c. $640
38. ZY
AUTO SALESA car lot has four sales associates.
35.
At the end of the year, each sales associate gets a ANSWER:
bonus of $1000 for every new car they have sold and undefined
$500 for every used car they have sold.
39. YZ
ANSWER:
40. (YX)Z
ANSWER:
a. Use a matrix to determine which sales associate
earned the most money.
b. What is the total amount of money the car lot
spent on bonuses for the sales associates this year?
ANSWER: (XZ)X
41.
ANSWER:
a. undefined
X(ZZ)
42.
b. $187,500 ANSWER:
Use matrices undefined
43. (XX)Z
to find
ANSWER:
each of the following. If the matrix does not
exist, write undefined.
XY
36.
CAMERASPrices of digital cameras depend on
44.
ANSWER: features like optical zoom, digital zoom, and
undefined megapixels.
YX
37.
ANSWER:
a. The 10-mp cameras are on sale for 20% off, and
38. ZY the other models are 10% off. Write a new matrix
for these changes.
ANSWER: b. Write a new matrix allowing for a 6.25% sales tax
undefined on the discounted prices.
YZ c. Describe what the differences in these two
39. matrices represent.
ANSWER:
ANSWER:
a.
(YX)Z
40.
ANSWER: b.
c. sales tax
41. (XZ)X
BUSINESSThe Kangy Studio has packages
45.
available for senior portraits.
ANSWER:
undefined
X(ZZ)
42.
ANSWER:
undefined
43. (XX)Z
ANSWER:
a. Use matrices to determine the total cost of each
CAMERASPrices of digital cameras depend on package.
44.
features like optical zoom, digital zoom, and b. The studio offers an early bird discount of 15% off
megapixels. any package. Find the early bird price for each
package.
ANSWER:
a. A: $421; B: $274; C: $150; D: $68
b. A: $357.85; B: $232.90; C: $127.50; D: $57.80
REASONING AB has
46. If the product matrix
A
a. The 10-mp cameras are on sale for 20% off, and dimensions 5 × 8, and has dimensions 5 × 6, what
the other models are 10% off. Write a new matrix are the dimensions of matrix B?
for these changes.
b. Write a new matrix allowing for a 6.25% sales tax ANSWER:
on the discounted prices. 6 × 8
c. Describe what the differences in these two
CCSS ARGUMENTSShow that each property of
matrices represent. 47.
matrices.
a. Scalar Distributive Property
ANSWER: b. Matrix Distributive Property
a. c. Associative Property of Multiplication
d. Associative Property of Scalar Multiplication
ANSWER:
a.
b.
c. sales tax
BUSINESSThe Kangy Studio has packages
45.
available for senior portraits.
b.
a. Use matrices to determine the total cost of each
package.
b. The studio offers an early bird discount of 15% off
any package. Find the early bird price for each
package.
ANSWER:
a. A: $421; B: $274; C: $150; D: $68
b. A: $357.85; B: $232.90; C: $127.50; D: $57.80
REASONING AB has
46. If the product matrix
A
dimensions 5 × 8, and has dimensions 5 × 6, what
are the dimensions of matrix B?
ANSWER:
c.
6 × 8
CCSS ARGUMENTSShow that each property of
47.
matrices.
a. Scalar Distributive Property
b. Matrix Distributive Property
c. Associative Property of Multiplication
d. Associative Property of Scalar Multiplication
ANSWER:
a.
d.
Substi
c(AB) =
Defini
c
=
Defini
=
b. Distri
=
Defini
=
Defini
= (cA)B Substi
Subst
c(AB) =
Defini
= c
Defini
=
Distri
=
c. Com
=
Defini
=
= A(cB) Substi
OPEN ENDEDWrite two matrices A and B such
48.
that AB = BA.
ANSWER:
d. Sample Answer:
Substi
c(AB) = CHALLENGE
Defini 49. Find the missing values in
c
=
Defini
ANSWER:
= a = 2, b = 1, c = 3, d = 4
Distri
WRITING IN MATHUse the data on Lisa Leslie
50.
= found at the beginning of the lesson to explain how
Defini matrices can be used in sports statistics. Describe a
matrix that represents the total number of points she
= has scored during her career and an example of a
Defini sport in which different point values are used in
scoring.
= (cA)B Substi
ANSWER:
Sports statistics are often listed in columns and
Subst matrices. In this case, you can find the total number
c(AB) = of points scored by multiplying the point value matrix,
Defini which does not change, by the scoring matrix, which
changes after each season. The total number of
= c points for her career can be found by multiplying the
Defini scoring matrix S by the point matrix P. Basketball
and wrestling use different point values in scoring.
=
GRIDDED RESPONSEThe average (arithmetic
Distri 51.
mean) of r, w, x, and y is 8, and the average of x and
= y is 4. What is the average of r and w?
Com
ANSWER:
= 12
Defini Carla, Meiko, and Kayla went shopping to get ready
52.
= for college. Their purchases and total amounts spent
= A(cB) Substi are shown in the table below.
OPEN ENDEDWrite two matrices A and B such
48.
that AB = BA.
ANSWER:
Sample Answer: Assume that all of the shirts were the same price, all
of the pants were the same price, and all of the shoes
were the same price. What was the price of each
CHALLENGE item?
49. Find the missing values in A
shirt, $12.95; pants, $15.99; shoes, $23.49
B
shirt, $15.99; pants, $12.95; shoes, $23.49
C
shirt, $15.99; pants, $23.49; shoes, $12.95
D
shirt, $23.49; pants, $15.99; shoes, $12.95
ANSWER:
a = 2, b = 1, c = 3, d = 4 ANSWER:
A
WRITING IN MATHUse the data on Lisa Leslie
50. GEOMETRY
found at the beginning of the lesson to explain how 53. Rectangle LMNQ has diagonals that
matrices can be used in sports statistics. Describe a intersect at point P. Which of the following
matrix that represents the total number of points she represents point P?
has scored during her career and an example of a
sport in which different point values are used in
scoring.
ANSWER:
F
Sports statistics are often listed in columns and (2, 2)
G
matrices. In this case, you can find the total number (1, 1)
of points scored by multiplying the point value matrix, H
(0, 0)
which does not change, by the scoring matrix, which J 1, 1)
(− −
changes after each season. The total number of
points for her career can be found by multiplying the ANSWER:
scoring matrix S by the point matrix P. Basketball H
and wrestling use different point values in scoring. SAT/ACT What are the dimensions of the matrix
54.
that results from the multiplication shown?
GRIDDED RESPONSEThe average (arithmetic
51.
mean) of r, w, x, and y is 8, and the average of x and
y is 4. What is the average of r and w?
ANSWER:
12
A
Carla, Meiko, and Kayla went shopping to get ready 1 × 4
52. B
for college. Their purchases and total amounts spent 3 × 3
C
are shown in the table below. 3 × 1
D
4 × 1
E
4 × 3
ANSWER:
D
Perform the indicated operations. If the matrix
does not exist, write impossible.
Assume that all of the shirts were the same price, all
of the pants were the same price, and all of the shoes
55.
were the same price. What was the price of each
item?
A ANSWER:
shirt, $12.95; pants, $15.99; shoes, $23.49
B
shirt, $15.99; pants, $12.95; shoes, $23.49
C
shirt, $15.99; pants, $23.49; shoes, $12.95
D
shirt, $23.49; pants, $15.99; shoes, $12.95
ANSWER:
A 56.
GEOMETRY Rectangle LMNQ has diagonals that
53.
intersect at point P. Which of the following ANSWER:
represents point P?
57.
F ANSWER:
(2, 2)
G
(1, 1)
H
(0, 0)
J 1, 1)
(− −
Solve each system of equations.
ANSWER:
H
SAT/ACT What are the dimensions of the matrix 58.
54.
that results from the multiplication shown?
ANSWER:
(–2, 5, 7)
A
1 × 4
B 59.
3 × 3
C
3 × 1 ANSWER:
D
4 × 1 (8, 3, 1)
E
4 × 3
ANSWER:
D
60.
Perform the indicated operations. If the matrix
does not exist, write impossible. ANSWER:
(–3, 2, –6)
55.
MEDICINEThe graph shows how much
61.
Americans spent on doctors visits in some recent
’
ANSWER: years and a prediction for 2014.
a. Find a regression equation for the data without the
predicted value.
b. Use your equation to predict the expenditures for
2014.
c. Compare your prediction to the one given in the
56. graph.
ANSWER:
57.
ANSWER:
ANSWER:
Solve each system of equations. a. Sample answer: y = 116.25x - 231,176.97
b. Sample answer: $2950.53 billion
c. The value predicted by the equation is significantly
lower than the one given in the graph.
58.
62. How many different ways can the letters of the word
ANSWER:
( 2, 5, 7) MATHEMATICS be arranged?
–
ANSWER:
4,989,600
Describe the transformation in each function.
Then graph the function.
59.
63.
ANSWER:
(8, 3, 1)
ANSWER:
Translated 4 units to the right and 3 units up.
60.
ANSWER:
(–3, 2, –6)
MEDICINEThe graph shows how much
61.
Americans spent on doctors visits in some recent
’
years and a prediction for 2014.
a. Find a regression equation for the data without the
predicted value.
b. Use your equation to predict the expenditures for 64.
2014.
ANSWER:
c. Compare your prediction to the one given in the Translated 3 units to the left and 5 units down and
graph. stretched vertically..
65.
ANSWER:
a. Sample answer: y = 116.25x - 231,176.97
b. Sample answer: $2950.53 billion ANSWER:
Translated 2 units to the left and 6 units down.
c. The value predicted by the equation is significantly
lower than the one given in the graph.
62. How many different ways can the letters of the word
MATHEMATICS be arranged?
ANSWER:
4,989,600
Describe the transformation in each function.
Then graph the function.
63.
ANSWER:
Translated 4 units to the right and 3 units up.
64.
ANSWER:
Translated 3 units to the left and 5 units down and
stretched vertically..
65.
ANSWER:
Translated 2 units to the left and 6 units down.
Determine whether each matrix product is
defined. If so, state the dimensions of the
product.
1.
ANSWER:
2×3
2.
ANSWER:
undefined
3.
ANSWER:
8×10
Find each product, if possible.
4.
ANSWER:
5.
ANSWER:
6.
ANSWER:
7.
ANSWER:
Determine whether each matrix product is
defined. If so, state the dimensions of the
product.
1.
8.
ANSWER:
ANSWER:
2×3 Undefined
2.
9.
ANSWER:
undefined ANSWER:
3.
ANSWER:
8×10
Find each product, if possible. 10.
4.
ANSWER:
ANSWER:
11.
5.
ANSWER: ANSWER:
12. CCSS SENSE-MAKINGThe table shows the
6. number of people registered for aerobics for the first
quarter.
ANSWER: Quinn’s Gym charges the following registration fees:
class-by-class, $165; 11-class pass, $110; unlimited
pass, $239.
7.
ANSWER:
a. Write a matrix for the registration fees and a
matrix for the number of students.
8. b. Find the total amount of money the gym received
from aerobics and step aerobic registrations.
ANSWER:
Undefined ANSWER:
a.
9.
b
. $22,955
ANSWER:
Use to
determine whether the following equations are
true for the given matrices.
10.
13. XY = YX
ANSWER:
ANSWER:
No;
14. X(YZ) = (XY)Z
ANSWER:
11.
Yes; and
ANSWER:
Determine whether each matrix product is
defined. If so, state the dimensions of the
12. CCSS SENSE-MAKINGThe table shows the product.
number of people registered for aerobics for the first
quarter. 15. P · Q
Quinn’s Gym charges the following registration fees: 2 × 3 3 × 4
class-by-class, $165; 11-class pass, $110; unlimited ANSWER:
pass, $239.
2×4
16. A · B
5 × 5 5 × 5
ANSWER:
5×5
a. Write a matrix for the registration fees and a 17. M3 × 1 · N2 × 3
matrix for the number of students.
b. Find the total amount of money the gym received ANSWER:
from aerobics and step aerobic registrations. undefined
18. X · Y
ANSWER: 2 × 6 6 × 3
a. ANSWER:
2×3
b 19. J · K
. $22,955 2 × 1 2 × 1
Use to ANSWER:
undefined
determine whether the following equations are 20. S · T
true for the given matrices. 5 × 2 2 × 4
ANSWER:
13. XY = YX
5×4
ANSWER:
No; Find each product, if possible.
21.
14. X(YZ) = (XY)Z ANSWER:
[ 26 ]
ANSWER:
Yes; and
22.
ANSWER:
Determine whether each matrix product is
defined. If so, state the dimensions of the
product.
15. P · Q 23.
2 × 3 3 × 4
ANSWER:
ANSWER:
2×4
16. A · B
5 × 5 5 × 5
24.
ANSWER:
5×5
ANSWER:
17. M3 × 1 · N2 × 3
ANSWER:
undefined
25.
18. X · Y
2 × 6 6 × 3
ANSWER:
ANSWER: Undefined
2×3
19. J · K
2 × 1 2 × 1
26.
ANSWER:
undefined
ANSWER:
20. S · T
5 × 2 2 × 4
ANSWER:
5×4
Find each product, if possible.
27.
21.
ANSWER:
ANSWER:
[ 26 ]
22. 28.
ANSWER: ANSWER:
3-6 Multiplying Matrices
TRAVEL The Wolf family owns three bed and
29.
23. breakfasts in a vacation spot. A room with a single
bed is $220 a night, a room with two beds is $250 a
night, and a suite is $360.
ANSWER:
24.
ANSWER:
a. Write a matrix for the number of each type of
room at each bed and breakfast. Then write a room-
cost matrix.
b. Write a matrix for total daily income, assuming
25. that all the rooms are rented.
c. What is the total daily income from all three bed
and breakfasts, assuming that all the rooms are
ANSWER: rented?
Undefined
ANSWER:
26. a.
ANSWER:
b.
c.
$5060
27. Use , and k
= 2 to determine whether the following
ANSWER:
equations are true for the given matrices.
30. k(PQ) = P(kQ)
ANSWER:
28. Yes;
ANSWER:
31. PQR = RQP
ANSWER:
TRAVEL The Wolf family owns three bed and No;
29.
breakfasts in a vacation spot. A room with a single
bed is $220 a night, a room with two beds is $250 a
night, and a suite is $360. 32. PR + QR = (P + Q)R
ANSWER:
eSolutions Manual - Powered by Cognero Page3
Yes;
33. R(P + Q) = PR + QR
ANSWER:
No;
a. Write a matrix for the number of each type of
room at each bed and breakfast. Then write a room-
CCSS SENSE-MAKINGStudent Council is selling
cost matrix. 34.
b. Write a matrix for total daily income, assuming flowers for Mother’s Day. They bought 200 roses,
that all the rooms are rented. 150 daffodils, and 100 orchids for the purchase prices
shown. They sold all of the flowers for the sales
c. What is the total daily income from all three bed prices shown.
and breakfasts, assuming that all the rooms are
rented?
ANSWER:
a.
b. a. Organize the data in two matrices, and use matrix
multiplication to find the total amount that was spent
on the flowers.
c. b. Write two matrices, and use matrix multiplication
$5060 to find the total amount the student council received
Use , and k for the flower sale.
c. Use matrix operations to find how much money
= 2 to determine whether the following the student council made on their project.
equations are true for the given matrices.
ANSWER:
a. $747.50
30. k(PQ) = P(kQ) b. $1387.50
c. $640
ANSWER:
Yes;
AUTO SALESA car lot has four sales associates.
35.
At the end of the year, each sales associate gets a
bonus of $1000 for every new car they have sold and
$500 for every used car they have sold.
31. PQR = RQP
ANSWER:
No;
32. PR + QR = (P + Q)R
ANSWER:
Yes;
a. Use a matrix to determine which sales associate
33. R(P + Q) = PR + QR earned the most money.
b. What is the total amount of money the car lot
ANSWER: spent on bonuses for the sales associates this year?
No;
ANSWER:
CCSS SENSE-MAKINGStudent Council is selling
34.
flowers for Mother’s Day. They bought 200 roses, a.
150 daffodils, and 100 orchids for the purchase prices
shown. They sold all of the flowers for the sales
prices shown. b. $187,500
Use matrices
to find
each of the following. If the matrix does not
exist, write undefined.
XY
36.
a. Organize the data in two matrices, and use matrix
multiplication to find the total amount that was spent ANSWER:
on the flowers. undefined
b. Write two matrices, and use matrix multiplication
to find the total amount the student council received YX
37.
for the flower sale.
ANSWER:
c. Use matrix operations to find how much money
the student council made on their project.
ANSWER:
a. $747.50
b. $1387.50 ZY
38.
c. $640
ANSWER:
AUTO SALESA car lot has four sales associates.
35. undefined
At the end of the year, each sales associate gets a
bonus of $1000 for every new car they have sold and YZ
39.
$500 for every used car they have sold.
ANSWER:
40. (YX)Z
ANSWER:
a. Use a matrix to determine which sales associate
earned the most money.
b. What is the total amount of money the car lot
spent on bonuses for the sales associates this year? 41. (XZ)X
ANSWER:
ANSWER:
undefined
X(ZZ)
a. 42.
ANSWER:
b. $187,500 undefined
Use matrices 43. (XX)Z
ANSWER:
to find
each of the following. If the matrix does not
exist, write undefined.
CAMERASPrices of digital cameras depend on
XY 44.
36. features like optical zoom, digital zoom, and
ANSWER: megapixels.
undefined
37. YX
ANSWER:
a. The 10-mp cameras are on sale for 20% off, and
the other models are 10% off. Write a new matrix
for these changes.
38. ZY b. Write a new matrix allowing for a 6.25% sales tax
on the discounted prices.
ANSWER:
undefined c. Describe what the differences in these two
matrices represent.
39. YZ
ANSWER:
ANSWER:
a.
40. (YX)Z b.
ANSWER:
c. sales tax
BUSINESSThe Kangy Studio has packages
45.
(XZ)X available for senior portraits.
41.
ANSWER:
undefined
X(ZZ)
42.
ANSWER:
undefined
43. (XX)Z
ANSWER:
a. Use matrices to determine the total cost of each
package.
b. The studio offers an early bird discount of 15% off
CAMERASPrices of digital cameras depend on
44. any package. Find the early bird price for each
features like optical zoom, digital zoom, and
megapixels. package.
ANSWER:
a. A: $421; B: $274; C: $150; D: $68
b. A: $357.85; B: $232.90; C: $127.50; D: $57.80
REASONING AB has
46. If the product matrix
A
dimensions 5 × 8, and has dimensions 5 × 6, what
are the dimensions of matrix B?
a. The 10-mp cameras are on sale for 20% off, and
the other models are 10% off. Write a new matrix ANSWER:
6 × 8
for these changes.
b. Write a new matrix allowing for a 6.25% sales tax
CCSS ARGUMENTSShow that each property of
on the discounted prices. 47.
matrices.
c. Describe what the differences in these two a. Scalar Distributive Property
matrices represent. b. Matrix Distributive Property
ANSWER: c. Associative Property of Multiplication
d. Associative Property of Scalar Multiplication
a.
ANSWER:
a.
b.
c. sales tax
BUSINESSThe Kangy Studio has packages
45.
available for senior portraits.
b.
a. Use matrices to determine the total cost of each
package.
b. The studio offers an early bird discount of 15% off
any package. Find the early bird price for each
package.
ANSWER:
a. A: $421; B: $274; C: $150; D: $68
b. A: $357.85; B: $232.90; C: $127.50; D: $57.80
REASONING AB has
46. If the product matrix
A
dimensions 5 × 8, and has dimensions 5 × 6, what
are the dimensions of matrix B? c.
ANSWER:
6 × 8
CCSS ARGUMENTSShow that each property of
47.
matrices.
a. Scalar Distributive Property
b. Matrix Distributive Property
c. Associative Property of Multiplication
d. Associative Property of Scalar Multiplication
ANSWER:
a. d.
Substi
c(AB) =
Defini
c
=
Defini
=
Distri
b. =
Defini
=
Defini
= (cA)B Substi
Subst
c(AB) =
Defini
= c
Defini
=
Distri
=
Com
c. =
Defini
=
= A(cB) Substi
OPEN ENDEDWrite two matrices A and B such
48.
that AB = BA.
ANSWER:
Sample Answer:
d.
Substi CHALLENGE
49. Find the missing values in
c(AB) =
Defini
c ANSWER:
= a = 2, b = 1, c = 3, d = 4
Defini
WRITING IN MATHUse the data on Lisa Leslie
= 50.
Distri found at the beginning of the lesson to explain how
matrices can be used in sports statistics. Describe a
= matrix that represents the total number of points she
Defini has scored during her career and an example of a
sport in which different point values are used in
= scoring.
Defini
ANSWER:
= (cA)B Substi Sports statistics are often listed in columns and
matrices. In this case, you can find the total number
Subst of points scored by multiplying the point value matrix,
which does not change, by the scoring matrix, which
c(AB) = changes after each season. The total number of
Defini points for her career can be found by multiplying the
scoring matrix S by the point matrix P. Basketball
= c and wrestling use different point values in scoring.
Defini
GRIDDED RESPONSEThe average (arithmetic
51.
= mean) of r, w, x, and y is 8, and the average of x and
Distri y is 4. What is the average of r and w?
= ANSWER:
Com 12
= 52. Carla, Meiko, and Kayla went shopping to get ready
Defini for college. Their purchases and total amounts spent
are shown in the table below.
=
= A(cB) Substi
OPEN ENDEDWrite two matrices A and B such
48.
that AB = BA.
Assume that all of the shirts were the same price, all
ANSWER: of the pants were the same price, and all of the shoes
Sample Answer: were the same price. What was the price of each
item?
A
shirt, $12.95; pants, $15.99; shoes, $23.49
B
CHALLENGE shirt, $15.99; pants, $12.95; shoes, $23.49
49. Find the missing values in C
shirt, $15.99; pants, $23.49; shoes, $12.95
D
shirt, $23.49; pants, $15.99; shoes, $12.95
ANSWER:
ANSWER: A
a = 2, b = 1, c = 3, d = 4
GEOMETRY Rectangle LMNQ has diagonals that
53.
WRITING IN MATHUse the data on Lisa Leslie
50. intersect at point P. Which of the following
found at the beginning of the lesson to explain how represents point P?
matrices can be used in sports statistics. Describe a
matrix that represents the total number of points she
has scored during her career and an example of a
sport in which different point values are used in
scoring.
F
(2, 2)
ANSWER: G
(1, 1)
Sports statistics are often listed in columns and H
matrices. In this case, you can find the total number (0, 0)
J 1, 1)
of points scored by multiplying the point value matrix, (− −
which does not change, by the scoring matrix, which ANSWER:
changes after each season. The total number of H
points for her career can be found by multiplying the SAT/ACT What are the dimensions of the matrix
scoring matrix S by the point matrix P. Basketball 54.
and wrestling use different point values in scoring. that results from the multiplication shown?
GRIDDED RESPONSEThe average (arithmetic
51.
mean) of r, w, x, and y is 8, and the average of x and
y is 4. What is the average of r and w?
ANSWER: A
12 1 × 4
B
3 × 3
C
Carla, Meiko, and Kayla went shopping to get ready 3 × 1
52. D
for college. Their purchases and total amounts spent 4 × 1
E
are shown in the table below. 4 × 3
ANSWER:
D
Perform the indicated operations. If the matrix
does not exist, write impossible.
Assume that all of the shirts were the same price, all 55.
of the pants were the same price, and all of the shoes
were the same price. What was the price of each ANSWER:
item?
A
shirt, $12.95; pants, $15.99; shoes, $23.49
B
shirt, $15.99; pants, $12.95; shoes, $23.49
C
shirt, $15.99; pants, $23.49; shoes, $12.95
D
shirt, $23.49; pants, $15.99; shoes, $12.95
56.
ANSWER:
A
ANSWER:
GEOMETRY Rectangle LMNQ has diagonals that
53.
intersect at point P. Which of the following
represents point P?
57.
ANSWER:
F
(2, 2)
G
(1, 1)
H
(0, 0) Solve each system of equations.
J 1, 1)
(− −
ANSWER:
H 58.
SAT/ACT What are the dimensions of the matrix ANSWER:
54. ( 2, 5, 7)
that results from the multiplication shown? –
59.
A
1 × 4
B ANSWER:
3 × 3 (8, 3, 1)
C
3 × 1
D
4 × 1
E
4 × 3
ANSWER: 60.
D
ANSWER:
Perform the indicated operations. If the matrix (–3, 2, –6)
does not exist, write impossible.
MEDICINEThe graph shows how much
61.
Americans spent on doctors visits in some recent
’
55. years and a prediction for 2014.
a. Find a regression equation for the data without the
ANSWER: predicted value.
b. Use your equation to predict the expenditures for
2014.
c. Compare your prediction to the one given in the
graph.
56.
ANSWER:
57.
ANSWER:
ANSWER:
a. Sample answer: y = 116.25x - 231,176.97
b. Sample answer: $2950.53 billion
Solve each system of equations. c. The value predicted by the equation is significantly
lower than the one given in the graph.
62. How many different ways can the letters of the word
58.
MATHEMATICS be arranged?
ANSWER:
ANSWER:
(–2, 5, 7) 4,989,600
Describe the transformation in each function.
Then graph the function.
63.
59.
ANSWER:
ANSWER: Translated 4 units to the right and 3 units up.
(8, 3, 1)
60.
ANSWER:
(–3, 2, –6)
MEDICINEThe graph shows how much
61.
Americans spent on doctors visits in some recent
’
years and a prediction for 2014.
a. Find a regression equation for the data without the 64.
predicted value.
b. Use your equation to predict the expenditures for ANSWER:
2014. Translated 3 units to the left and 5 units down and
stretched vertically..
c. Compare your prediction to the one given in the
graph.
65.
ANSWER:
ANSWER: Translated 2 units to the left and 6 units down.
a. Sample answer: y = 116.25x - 231,176.97
b. Sample answer: $2950.53 billion
c. The value predicted by the equation is significantly
lower than the one given in the graph.
62. How many different ways can the letters of the word
MATHEMATICS be arranged?
ANSWER:
4,989,600
Describe the transformation in each function.
Then graph the function.
63.
ANSWER:
Translated 4 units to the right and 3 units up.
64.
ANSWER:
Translated 3 units to the left and 5 units down and
stretched vertically..
65.
ANSWER:
Translated 2 units to the left and 6 units down.
Determine whether each matrix product is
defined. If so, state the dimensions of the
product.
1.
ANSWER:
2×3
2.
ANSWER:
undefined
3.
ANSWER:
8×10
Find each product, if possible.
4.
ANSWER:
5.
ANSWER:
6.
Determine whether each matrix product is
defined. If so, state the dimensions of the ANSWER:
product.
1.
7.
ANSWER:
2×3
ANSWER:
2.
ANSWER:
undefined
8.
3.
ANSWER:
ANSWER: Undefined
8×10
Find each product, if possible. 9.
4.
ANSWER:
ANSWER:
10.
5.
ANSWER:
ANSWER:
11.
6.
ANSWER:
ANSWER:
7.
12. CCSS SENSE-MAKINGThe table shows the
ANSWER: number of people registered for aerobics for the first
quarter.
Quinn’s Gym charges the following registration fees:
class-by-class, $165; 11-class pass, $110; unlimited
pass, $239.
8.
ANSWER:
Undefined
9.
a. Write a matrix for the registration fees and a
matrix for the number of students.
ANSWER: b.
Find the total amount of money the gym received
from aerobics and step aerobic registrations.
ANSWER:
10. a.
b
. $22,955
ANSWER:
Use to
determine whether the following equations are
true for the given matrices.
13. XY = YX
11.
ANSWER:
No;
ANSWER:
14. X(YZ) = (XY)Z
ANSWER:
12. CCSS SENSE-MAKINGThe table shows the
number of people registered for aerobics for the first Yes; and
quarter.
Quinn’s Gym charges the following registration fees:
class-by-class, $165; 11-class pass, $110; unlimited
pass, $239.
Determine whether each matrix product is
defined. If so, state the dimensions of the
product.
15. P · Q
2 × 3 3 × 4
a. Write a matrix for the registration fees and a ANSWER:
matrix for the number of students. 2×4
b. Find the total amount of money the gym received
from aerobics and step aerobic registrations. 16. A · B
5 × 5 5 × 5
ANSWER:
ANSWER:
a. 5×5
17. M3 × 1 · N2 × 3
b
. $22,955
ANSWER:
Use to undefined
determine whether the following equations are 18. X · Y
2 × 6 6 × 3
true for the given matrices.
ANSWER:
2×3
13. XY = YX
ANSWER: 19. J · K
2 × 1 2 × 1
No;
ANSWER:
undefined
20. S · T
14. X(YZ) = (XY)Z 5 × 2 2 × 4
ANSWER:
ANSWER:
Yes; and 5×4
Find each product, if possible.
21.
Determine whether each matrix product is
defined. If so, state the dimensions of the ANSWER:
product. [ 26 ]
15. P · Q
2 × 3 3 × 4
22.
ANSWER:
ANSWER:
2×4
16. A · B
5 × 5 5 × 5
ANSWER:
23.
5×5
17. M3 × 1 · N2 × 3 ANSWER:
ANSWER:
undefined
18. X · Y
2 × 6 6 × 3
24.
ANSWER:
ANSWER:
2×3
19. J · K
2 × 1 2 × 1
ANSWER:
undefined
25.
20. S · T
5 × 2 2 × 4
ANSWER:
Undefined
ANSWER:
5×4
Find each product, if possible. 26.
21.
ANSWER:
ANSWER:
[ 26 ]
22.
27.
ANSWER:
ANSWER:
23.
28.
ANSWER:
ANSWER:
24. TRAVEL The Wolf family owns three bed and
29.
breakfasts in a vacation spot. A room with a single
ANSWER: bed is $220 a night, a room with two beds is $250 a
night, and a suite is $360.
25.
ANSWER:
Undefined
a. Write a matrix for the number of each type of
room at each bed and breakfast. Then write a room-
26. cost matrix.
b. Write a matrix for total daily income, assuming
that all the rooms are rented.
ANSWER:
c. What is the total daily income from all three bed
and breakfasts, assuming that all the rooms are
rented?
ANSWER:
27. a.
ANSWER:
b.
c.
$5060
28. Use , and k
ANSWER: = 2 to determine whether the following
equations are true for the given matrices.
30. k(PQ) = P(kQ)
TRAVEL The Wolf family owns three bed and
29.
breakfasts in a vacation spot. A room with a single ANSWER:
bed is $220 a night, a room with two beds is $250 a Yes;
night, and a suite is $360.
31. PQR = RQP
ANSWER:
No;
32. PR + QR = (P + Q)R
a. Write a matrix for the number of each type of
room at each bed and breakfast. Then write a room- ANSWER:
cost matrix. Yes;
b. Write a matrix for total daily income, assuming
that all the rooms are rented.
33. R(P + Q) = PR + QR
c. What is the total daily income from all three bed
and breakfasts, assuming that all the rooms are
rented? ANSWER:
No;
ANSWER:
CCSS SENSE-MAKINGStudent Council is selling
34.
a. flowers for Mother s Day. They bought 200 roses,
’
150 daffodils, and 100 orchids for the purchase prices
shown. They sold all of the flowers for the sales
prices shown.
b.
c.
$5060
Use , and k
= 2 to determine whether the following
equations are true for the given matrices. a. Organize the data in two matrices, and use matrix
multiplication to find the total amount that was spent
30. k(PQ) = P(kQ) on the flowers.
b. Write two matrices, and use matrix multiplication
ANSWER: to find the total amount the student council received
Yes; for the flower sale.
c. Use matrix operations to find how much money
the student council made on their project.
31. PQR = RQP
ANSWER:
ANSWER: a. $747.50
3-6 Multiplying Matrices b. $1387.50
No;
c. $640
PR+QR=(P+Q)R AUTO SALESA car lot has four sales associates.
32. 35.
At the end of the year, each sales associate gets a
ANSWER: bonus of $1000 for every new car they have sold and
Yes; $500 for every used car they have sold.
33. R(P + Q) = PR + QR
ANSWER:
No;
CCSS SENSE-MAKINGStudent Council is selling
34.
flowers for Mother’s Day. They bought 200 roses,
150 daffodils, and 100 orchids for the purchase prices
shown. They sold all of the flowers for the sales a. Use a matrix to determine which sales associate
prices shown. earned the most money.
b. What is the total amount of money the car lot
spent on bonuses for the sales associates this year?
ANSWER:
a.
a. Organize the data in two matrices, and use matrix b. $187,500
multiplication to find the total amount that was spent
on the flowers. Use matrices
b. Write two matrices, and use matrix multiplication
to find the total amount the student council received to find
for the flower sale.
c. Use matrix operations to find how much money each of the following. If the matrix does not
the student council made on their project. exist, write undefined.
XY
36.
ANSWER:
a. $747.50 ANSWER:
b. $1387.50 undefined
c. $640
37. YX
AUTO SALESA car lot has four sales associates.
35.
At the end of the year, each sales associate gets a ANSWER:
bonus of $1000 for every new car they have sold and
$500 for every used car they have sold.
38. ZY
ANSWER:
undefined
39. YZ
ANSWER:
eSolutions Manual - Powered by Cognero Page4
a. Use a matrix to determine which sales associate
earned the most money.
b. What is the total amount of money the car lot
spent on bonuses for the sales associates this year?
ANSWER: 40. (YX)Z
ANSWER:
a.
b. $187,500
Use matrices 41. (XZ)X
ANSWER:
to find undefined
X(ZZ)
each of the following. If the matrix does not 42.
exist, write undefined.
XY ANSWER:
36. undefined
ANSWER:
undefined 43. (XX)Z
ANSWER:
37. YX
ANSWER:
CAMERASPrices of digital cameras depend on
44.
features like optical zoom, digital zoom, and
megapixels.
38. ZY
ANSWER:
undefined
YZ
39.
ANSWER: a. The 10-mp cameras are on sale for 20% off, and
the other models are 10% off. Write a new matrix
for these changes.
b. Write a new matrix allowing for a 6.25% sales tax
on the discounted prices.
(YX)Z c. Describe what the differences in these two
40. matrices represent.
ANSWER:
ANSWER:
a.
(XZ)X
41.
ANSWER: b.
undefined
X(ZZ)
42.
c. sales tax
ANSWER:
undefined
BUSINESSThe Kangy Studio has packages
45.
(XX)Z available for senior portraits.
43.
ANSWER:
CAMERASPrices of digital cameras depend on
44.
features like optical zoom, digital zoom, and
megapixels.
a. Use matrices to determine the total cost of each
package.
b. The studio offers an early bird discount of 15% off
any package. Find the early bird price for each
a. The 10-mp cameras are on sale for 20% off, and
the other models are 10% off. Write a new matrix package.
ANSWER:
for these changes.
b. Write a new matrix allowing for a 6.25% sales tax a. A: $421; B: $274; C: $150; D: $68
on the discounted prices. b. A: $357.85; B: $232.90; C: $127.50; D: $57.80
c. Describe what the differences in these two REASONING AB has
matrices represent. 46. If the product matrix
A
dimensions 5 × 8, and has dimensions 5 × 6, what
ANSWER: are the dimensions of matrix B?
a. ANSWER:
6 × 8
CCSS ARGUMENTSShow that each property of
47.
matrices.
b. a. Scalar Distributive Property
b. Matrix Distributive Property
c. Associative Property of Multiplication
d.
Associative Property of Scalar Multiplication
c. sales tax
ANSWER:
a.
BUSINESSThe Kangy Studio has packages
45.
available for senior portraits.
b.
a. Use matrices to determine the total cost of each
package.
b. The studio offers an early bird discount of 15% off
any package. Find the early bird price for each
package.
ANSWER:
a. A: $421; B: $274; C: $150; D: $68
b. A: $357.85; B: $232.90; C: $127.50; D: $57.80
REASONING AB has
46. If the product matrix
A
dimensions 5 × 8, and has dimensions 5 × 6, what
are the dimensions of matrix B?
ANSWER:
6 × 8
CCSS ARGUMENTSShow that each property of
47.
matrices.
a. Scalar Distributive Property
b. Matrix Distributive Property
c. Associative Property of Multiplication
c.
d. Associative Property of Scalar Multiplication
ANSWER:
a.
d.
Substi
b. c(AB) =
Defini
c
=
Defini
=
Distri
=
Defini
=
Defini
= (cA)B Substi
Subst
c(AB) =
Defini
c. = c
Defini
=
Distri
=
Com
=
Defini
=
d. = A(cB) Substi
Substi
c(AB) =
Defini 48. OPEN ENDEDWrite two matrices A and B such
that AB = BA.
c ANSWER:
=
Defini Sample Answer:
=
Distri CHALLENGE
49. Find the missing values in
=
Defini
= ANSWER:
Defini a = 2, b = 1, c = 3, d = 4
= (cA)B Substi 50. WRITING IN MATHUse the data on Lisa Leslie
found at the beginning of the lesson to explain how
matrices can be used in sports statistics. Describe a
Subst matrix that represents the total number of points she
c(AB) = has scored during her career and an example of a
Defini sport in which different point values are used in
scoring.
= c
Defini ANSWER:
= Sports statistics are often listed in columns and
Distri matrices. In this case, you can find the total number
of points scored by multiplying the point value matrix,
= which does not change, by the scoring matrix, which
Com changes after each season. The total number of
points for her career can be found by multiplying the
= scoring matrix S by the point matrix P. Basketball
Defini and wrestling use different point values in scoring.
51. GRIDDED RESPONSEThe average (arithmetic
= mean) of r, w, x, and y is 8, and the average of x and
= A(cB) Substi y is 4. What is the average of r and w?
ANSWER:
12
48. OPEN ENDEDWrite two matrices A and B such
that AB = BA. 52. Carla, Meiko, and Kayla went shopping to get ready
for college. Their purchases and total amounts spent
ANSWER: are shown in the table below.
Sample Answer:
CHALLENGE
49. Find the missing values in
Assume that all of the shirts were the same price, all
ANSWER: of the pants were the same price, and all of the shoes
a = 2, b = 1, c = 3, d = 4 were the same price. What was the price of each
item?
50. WRITING IN MATHUse the data on Lisa Leslie A
found at the beginning of the lesson to explain how shirt, $12.95; pants, $15.99; shoes, $23.49
B
matrices can be used in sports statistics. Describe a shirt, $15.99; pants, $12.95; shoes, $23.49
C
matrix that represents the total number of points she shirt, $15.99; pants, $23.49; shoes, $12.95
D
has scored during her career and an example of a shirt, $23.49; pants, $15.99; shoes, $12.95
sport in which different point values are used in
scoring. ANSWER:
A
53. GEOMETRY Rectangle LMNQ has diagonals that
ANSWER: intersect at point P. Which of the following
Sports statistics are often listed in columns and represents point P?
matrices. In this case, you can find the total number
of points scored by multiplying the point value matrix,
which does not change, by the scoring matrix, which
changes after each season. The total number of
points for her career can be found by multiplying the
scoring matrix S by the point matrix P. Basketball
and wrestling use different point values in scoring. F
(2, 2)
G
(1, 1)
GRIDDED RESPONSEThe average (arithmetic
51. H
mean) of r, w, x, and y is 8, and the average of x and (0, 0)
J 1, 1)
y is 4. What is the average of r and w? (− −
ANSWER:
ANSWER: H
12
SAT/ACT What are the dimensions of the matrix
Carla, Meiko, and Kayla went shopping to get ready 54.
52. that results from the multiplication shown?
for college. Their purchases and total amounts spent
are shown in the table below.
A
1 × 4
B
3 × 3
C
3 × 1
D
Assume that all of the shirts were the same price, all 4 × 1
E
of the pants were the same price, and all of the shoes 4 × 3
were the same price. What was the price of each
item? ANSWER:
A D
shirt, $12.95; pants, $15.99; shoes, $23.49
B
shirt, $15.99; pants, $12.95; shoes, $23.49 Perform the indicated operations. If the matrix
C
shirt, $15.99; pants, $23.49; shoes, $12.95 does not exist, write impossible.
D
shirt, $23.49; pants, $15.99; shoes, $12.95
55.
ANSWER:
A
ANSWER:
GEOMETRY Rectangle LMNQ has diagonals that
53.
intersect at point P. Which of the following
represents point P?
56.
ANSWER:
F
(2, 2)
G
(1, 1)
H
(0, 0)
J 1, 1)
(− −
57.
ANSWER:
H
ANSWER:
SAT/ACTWhat are the dimensions of the matrix
54.
that results from the multiplication shown?
Solve each system of equations.
A 58.
1 × 4
B
3 × 3
C ANSWER:
3 × 1 ( 2, 5, 7)
D –
4 × 1
E
4 × 3
ANSWER:
D
59.
Perform the indicated operations. If the matrix
does not exist, write impossible. ANSWER:
(8, 3, 1)
55.
ANSWER:
60.
ANSWER:
(–3, 2, –6)
MEDICINEThe graph shows how much
61.
56. Americans spent on doctors visits in some recent
’
years and a prediction for 2014.
a.
ANSWER: Find a regression equation for the data without the
predicted value.
b. Use your equation to predict the expenditures for
2014.
c. Compare your prediction to the one given in the
graph.
57.
ANSWER:
Solve each system of equations.
58.
ANSWER:
( 2, 5, 7) ANSWER:
– a. Sample answer: y = 116.25x - 231,176.97
b. Sample answer: $2950.53 billion
c. The value predicted by the equation is significantly
lower than the one given in the graph.
59. How many different ways can the letters of the word
62.
MATHEMATICS be arranged?
ANSWER:
(8, 3, 1)
ANSWER:
4,989,600
Describe the transformation in each function.
Then graph the function.
60.
63.
ANSWER:
(–3, 2, –6)
ANSWER:
Translated 4 units to the right and 3 units up.
MEDICINEThe graph shows how much
61.
Americans spent on doctors visits in some recent
’
years and a prediction for 2014.
a. Find a regression equation for the data without the
predicted value.
b. Use your equation to predict the expenditures for
2014.
c. Compare your prediction to the one given in the
graph.
64.
ANSWER:
Translated 3 units to the left and 5 units down and
stretched vertically..
ANSWER:
a. Sample answer: y = 116.25x - 231,176.97
b. Sample answer: $2950.53 billion
c. The value predicted by the equation is significantly
lower than the one given in the graph.
62. How many different ways can the letters of the word
65.
MATHEMATICS be arranged?
ANSWER:
ANSWER:
4,989,600 Translated 2 units to the left and 6 units down.
Describe the transformation in each function.
Then graph the function.
63.
ANSWER:
Translated 4 units to the right and 3 units up.
64.
ANSWER:
Translated 3 units to the left and 5 units down and
stretched vertically..
65.
ANSWER:
Translated 2 units to the left and 6 units down.
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