Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM.
75)
Hurst’s Feed & Seed sold to one customer 5 bushels of wheat, 2 of corn, and 3 of rye, for $31.00. To
another customer he sold 2 bushels of wheat, 3 of corn, and 5 of rye, for $27.60. To a third customer
he sold 3 bushels of wheat, 5 of corn, and 2 of rye for $32.70. What was the price per bushel for
each of the different grains?
Let x represent the price per bushel for wheat, y the price per bushel for corn, and z the price per
bushel for rye.
75)
A)
5x + 2y + 3z = 31.00
2x + 3y + 5z = 27.60
3x + 5y + 2z = 32.70
B)
5x + 2y + 3z = 31.00
2x – 3y + 5z = 27.60
3x + 5y + 2z = 32.70
C)
5x + 2y + 3z = 31.00
2x + 3y – 5z = 27.60
3x + 5y – 2z = 32.70
D)
5x + 2y – 3z = 31.00
2x + 3y – 5z = 27.60
3x + 5y – 2z = 32.70
Perform the operation, if possible.
76)
A =3-1
5 0 , B =0-1
3 6 Find AB.
76)
A)
0 1
15 0
B)
-3 -9
0-5
C)
-5 0
39 -3
D)
-9 -3
-5 0
77)
–9 1
2 5
+6 2
2–3
77)
A)
–3–7
–7–12
B)
–3 3
4 2
C)
3 3
4 2
D)
–3–3
4 2
Solve the system as matrix equations using inverses.
78)
–5x1+ 3x2= 8
3x1– 6x2= – 30
78)
A)
(–6, –2)
B)
(–2, –6)
C)
(6, 2)
D)
(2, 6)
21
Use the given encoding matrix A to solve the problem.
79)
A message has been encoded and the matrix which the receiver gets is shown below.
The encoding matrix A which was used to encode the message is:
A =0 2
3 1
Find the decoding matrix A–1, and use it to decode the message.
Assume that the numerical assignment used was a = 1, b = 2, ….., z = 26, space = 30, period = 40,
and apostrophe = 60.
79)
A)
DRINK ENOUGH MILK
B)
EAT YOUR VEGETABLES
C)
EAT YOUR BROCCOLI
D)
DRINK ENOUGH COKE
Solve using Gauss–Jordan elimination.
80)
9x – y + 6z = 50
–7x + 5y – 2z = – 4
-4x – 5y + z =-53
80)
A)
(5, 2, 7)
B)
(5, 7, 2)
C)
(-5, 7, 10)
D)
No solution
User row operations to change the matrix to reduced form.
81)
1 0 2
–1 1 3
81)
A)
1 0 2
0 0 5
B)
0 1 5
–1 1 3
C)
1 0 2
0 1 5
D)
1 0 2
–1 1 3
Perform the indicated operations given the matrices.
82)
Let C =
1
–3
2
and D =
–1
3
–2
; C – 2D
82)
A)
3
–6
4
B)
-3
9
-6
C)
-1
3
-2
D)
3
-9
6
Identify the row operation that produces the resulting matrix.
83)
3 0 15
–2 4 12 3 0 15
0 2 11
83)
A)
1
3R1+R2
R1
B)
1
3R1+1
2R2
R2
C)
1
2R1+1
3R2
R1
D)
R1+1
2R2
R2
Find the values of a, b, c, and d that make the matrix equation true.
84)
1 2
0–1
a b
c d
=1 2
2 4
84)
A)
1 0
0 1
B)
0 0
2 5
C)
2 1
4 2
D)
5 10
–2–4
Solve the problem.
85)
A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the number
of units of each ingredient in each type of candy in one batch. Matrix B gives the cost of each
ingredient (dollars per unit) from suppliers X and Y. What is the cost of 100 batches from supplier
X?
85)
A)
$7800
B)
$4800
C)
$6600
D)
$3300
Solve the system of equations by elimination.
86)
2x – 7y= – 20
-7x + 3y=27
86)
A)
(–3, -2)
B)
(3, 2)
C)
(3, -2)
D)
(–3, 2)
Write the system as a matrix equation of the form AX = B.
87)
8x1+ 9x2= 117
4x1+ 6x2= 66
87)
A)
8 4
9 6
x1
x2
=117
66
B)
8 9
4 6
x1
x2
=117
66
C)
8 9
6 4
x1
x2
=66
117
D)
117 9
66 6
x1
x2
=8
6
24
The matrix is the final matrix form for a system of two linear equations in variables x1 and x2. Write the Solution of the
system.
88)
1–410
0 0 0
88)
A)
x1= t for any real number t
x2= 10
B)
No solution
C)
x1= 4t + 10
x2= t for any real number t
D)
x1= t – 4
x2= t for any real number t
Solve the problem.
89)
Your screen print operation is doing extremely well at the craft shows. Last week you sold 50
tie–dyed shirts for $15 each, 40 Cheraw–Tech crew shirts for $10 each and 30 handpainted T–shirts
for $12 each. Use matrix operations to calculate your total revenue for the week.
89)
A)
$1480
B)
$1750
C)
$1151
D)
$1510
Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM.
90)
There were 35,000 people at a ball game in Atlanta. The day’s receipts were $290,000. How many
people paid $14 for reserved seats and how many paid $6 for general admission? Let x represent
the number of reserved seats and y represent the number of general admission seats.
90)
A)
14x + 6y = 105
x + y = 35,000
B)
25,000x + 14y = 35,000
x + y = 290,000
C)
15,000x + 14y = 20,000
x + y = 6
D)
20,000x + 14y = 6
x + y = 15,000
Provide an appropriate response.
91)
Use the augmented matrix to solve the system:
0.4x1+ 0.9x2= – 4.9
x1– 0.3x2= 0.5
91)
A)
(0, 0)
B)
(–0.1, –0.5)
C)
(–5, –1)
D)
(–1, –5)
Solve using Gauss–Jordan elimination.
92)
x + y + z =-2
x – y + 5z = 6
2x + y + z =-3
92)
A)
(1, -1, -2)
B)
(-1, -2, 1)
C)
(1, -2, -1)
D)
No solution
Write the system as a matrix equation of the form AX = B.
93)
6x1+ 4x2= 30
8x2= 72
93)
A)
6 4
872
x1
x2
=30
0
B)
30 4
72 0
x1
x2
=6
8
C)
8 0
6 4
x1
x2
=72
4
D)
6 4
0 8
x1
x2
=30
72
Perform the operation, if possible.
94)
– 1 0
3 1
––1 3
3 1
94)
A)
–2 3
6 2
B)
–3
C)
0 3
0 0
D)
0–3
0 0
Find the inverse, if it exists, of the given matrix.
95)
5 6
4 5
95)
A)
5-6
-4 5
B)
5 4
6 5
C)
–5-6
-4 –5
D)
–5 4
6–5
Solve using Gauss–Jordan elimination.
96)
4x – 2y = 7
8x – 4y = 1
96)
A)
(2, 2)
B)
– 2
7x + 4
7y, y
C)
(7, 1)
D)
No solution
Perform the operation, if possible.
97)
Let A =
1 8
-8 1
-8 -9
and B =
4 1
-7 4
2 8
. Find A + B.
97)
A)
5 9
15 1
-6 1
B)
-3 7
–1–1
-10 -16
C)
5 9
-15 5
-6 -1
D)
5 1
-15 5
-6 -1
Solve the equation for the indicated variable. Assume that the dimensions are such that matrix multiplication and
addition are possible and that inverses exist when needed.
98)
Solve for C: CZ = Y
98)
A)
C = Y/Z
B)
C =Z–1Y
C)
C = YZ–1
D)
C = ZY–1
Solve the system as matrix equations using inverses.
99)
A company produces three models of MP3 players, models A, B, and C. Each model A machine
requires 3.2 hours of electronics work, 2.8 hours of assembly time, and 4.4 hours of quality
assurance time. Each model B machine requires 5.4 hours of electronics work, 2.4 hours of assembly
time, and 3.4 hours of quality assurance time. Each model C machine requires 2.2 hours of
electronics work, 5.8 hours of assembly time, and 4.8 hours of quality assurance time. There are
303 hours available each week for electronics, 393 hours for assembly, and 416 hours for quality
assurance. How many of each model should be produced each week if all available time must be
used?
99)
A)
Model A: 30
Model B: 20
Model C: 45
B)
Model A: 28
Model B: 22
Model C: 45
C)
Model A: 31
Model B: 20
Model C: 44
D)
Model A: 30
Model B: 15
Model C: 50
Solve the problem.
100)
Two sectors of a textbook economy are (1) communication equipment and (2) components and
accessories. In 2005 the input–output table involving these two sectors was as follows.
To Equipment Components
From Equipment 6,000 500
Components 24,000 30,000
Total Output 90,000 140,000
Determine the production levels necessary in these two sectors to meet a demand for $80,000 of
equipment and $90,000 of components. Round to significant digits.
100)
A)
Equipment: 90,000
Components: 140,000
B)
Equipment: 86,000
Components: 90,000
C)
Equipment: 86,000
Components: 140,000
D)
Equipment: 24,000
Components: 140,000
101)
A chemistry department wants to make 3 liters of a 17.5% basic solution by mixing a 20% solution
with a 15% solution. How many liters of each type of basic solution should be used to produce the
17.5% solution?
101)
A)
2 liters of 15% solution, 1 liter of 20% solution
B)
0.5 liter of 15% solution, 2.5 liters of 20% solution
C)
1 liter of 15% solution, 2 liters of 20% solution
D)
1.5 liters of 15% solution, 1.5 liters of 20% solution
Write the linear system corresponding to the reduced augmented matrix.
102)
100 4
011 6
0 0 0 0
102)
A)
x1= 4, x2= – t + 6, x3= t for any real number t
B)
x1= – 4, x2= t + 6, x3= t for any real number t
C)
No Solution
D)
x1= 4, x2= t + 6, x3= 0
Solve using Gauss–Jordan elimination.
103)
x1+x2= 0
x1– x 2 = 12
103)
A)
(–6, –5)
B)
(–5, –6)
C)
(5, –5)
D)
(6, –6)
D
Solve the system of equations by elimination.
104)
5x + y =-23
3x – y =7
104)
A)
(-2, -13)
B)
(-13, -2)
C)
infinitely many solutions
D)
no solution
A
Solve the problem.
105)
Daisy has a desk full of quarters and nickels. If she has a total of 23 coins with a total face value of
$4.35, how many of the coins are nickels?
105)
A)
16 nickels
B)
9 nickels
C)
21 nickels
D)
7 nickels
D
A
Perform the indicated operations given the matrices.
106)
Let A =1 3
2 6 and B =0 4
–1 6 ; 3A + B
106)
A)
3 7
512
B)
321
336
C)
313
112
D)
313
524
Solve the problem.
107)
A textbook economy has only two industries, the electric company and the gas company. Each
dollar’s worth of the electric company’s output requires 0.20 of its own output and 0.4 of the gas
company’s output. Each dollar’s worth of the gas company’s output requires 0.50 of its own output
and 0.7 of the electric company’s output. What should the production of electricity and gas be (in
dollars) if there is a $16 M demand for electricity and a $7 M demand for gas?
107)
A)
Electricity: $125 M; Gas: $92.5 M
B)
Electricity: $115 M; Gas: $103.5 M
C)
Electricity: $97.5 M; Gas: $103 M
D)
Electricity: $107.5 M; Gas: $100 M
Determine whether B is the inverse of A.
108)
A =5 3
3 2 , B =2–3
–3 5
108)
A)
Yes
B)
No
Provide an appropriate response.
109)
Determine the value of each variable.
x + 3 y + 4
7 –1
=6 0
7 k
109)
A)
x = 3
y = – 4
k = – 1
B)
x = 6
y = 0
k = – 1
C)
x = – 3
y = 4
k = – 1
D)
x = – 3
y = – 4
k = – 1
Solve the system as matrix equations using inverses.
110)
– 2x1+ 6x2= 6
3x1+ 2x2= 13
110)
A)
(–2, –3)
B)
(–3 , – 2)
C)
(2,3)
D)
(3,2)
Identify the row operation that produces the resulting matrix.
111)
1–3 4
2 3 1
1–3 4
–1–6 3
111)
A)
R1+ (–1)R2
R2
B)
(–1)R1+R2
R2
C)
(–1)R2
R2
D)
R1+ (–1)R2
R1
Solve the system of equations by graphing.
112)
2x – y =8
y=-2
112)
A)
(-3, 2)
B)
(-2, 3)
C)
(3, -2)
D)
no solution
Find the inverse, if it exists, of the given matrix.
113)
1 1 1
2 1 1
2 2 3
113)
A)
–1 1 0
4–1–1
–2 0 1
B)
1 1 1
1
2 1 1
1
2
1
2
1
3
C)
–1–1–1
–2–1–1
–2–2–3
D)
Does not exist
114)
–6–6
–5–5
114)
A)
–5
11 –6
11
–5
11 –6
11
B)
–5
11
6
11
5
11 –6
11
C)
5
11 –6
11
–5
11
6
11
D)
Does not exist
Solve using Gauss–Jordan elimination.
115)
6x + 2y = – 6
4x + 6y = 24
115)
A)
(6, -3)
B)
(-3, 6)
C)
(-3, -6)
D)
No solution
User row operations to change the matrix to reduced form.
116)
1–1 0 1
0 4 8 4
0 0 0 0
116)
A)
1 0 2 2
0 1 2 1
0 0 0 0
B)
1 0 2 2
0 1 2 0
0 0 0 0
C)
1–1 0 1
0 1 2 1
0 0 0 0
D)
1 0 2 0
0 1 2 1
0 0 0 0
Solve the system as matrix equations using inverses.
117)
There were 340 people at a play. The admission price was $2 for adults and $1 for children. The
admission receipts were $490. How many adults and how many children attended?
117)
A)
95 adults and 245 children
B)
150 adults and 190 children
C)
122 adults and 218 children
D)
190 adults and 150 children
Provide an appropriate response.
118)
Given the matrix B:
B =
–3
–1
1
What is the size of B?
118)
A)
1 × 1
B)
3
C)
1 × 3
D)
3 × 1
Solve the problem.
119)
The input–output matrix for an economy is
Output:
Agri. Mfg.
Input: Agri.
Mfg.
0.04 0.18
0.02 0.22
= T
The demand matrix is D = 700
1000
Find the internal consumption.
119)
A)
161.5
108.3
B)
274.2
307.0
C)
374.2
397.3
D)
507.2
57.0
Provide an appropriate response.
120)
Write the augmented matrix for the system.
8x1+ 9x2= 117
4x1+ 6x2= 66
120)
A)
8 4 117
9 6 66
B)
117 9 8
66 4 6
C)
8 9 66
6 4 117
D)
8 9 117
4 6 66
Perform the operation, if possible.
121)
Let C =
1
– 3
2
and D =
– 1
3
– 2
. Find C – 4D.
121)
A)
5
–15
10
B)
– 5
15
–10
C)
–3
9
–6
D)
5
–6
4
Solve the problem.
122)
Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%.
The total income from all 3 investments is $1600. The income from the 5% and 6% investments is
the same as the income from the 8% investment. Find the amount invested at each rate.
122)
A)
$10,000 at 5%, $5000 at 6%, $10,000 at 8%
B)
$10,000 at 5%, $10,000 at 6%, $5000 at 8%
C)
$8000 at 5%, $10,000 at 6%, $7000 at 8%
D)
$5000 at 5%, $10,000 at 6%, $10,000 at 8%
Provide an appropriate response.
123)
Solve the linear system corresponding to the following augmented matrix:
3 6 24
2 3 11
123)
A)
(5, –2)
B)
(–2, 5)
C)
(–2, –5)
D)
(0, 0)
Find the values of a, b, c, and d that make the matrix equation true.
124)
a b
c d
+ 0 5
–4 7
=3 7
2–1
124)
A)
3 2
6–8
B)
–3–2
–6 8
C)
0 2
6 8
D)
3 12
–2 6
Find the matrix product mentally, without the use of a calculator or pencil–and–paper calculations.
125)
1 0
0 1
2 3
5 1
125)
A)
2 3
5 1
B)
1 1
1 1
C)
1
2
1
3
1
51
D)
3 2
1 5
Solve the system of equations by graphing.
126)
2x +y=-3
3x +y=-5
126)
A)
(1, -2)
B)
(-2, 1)
C)
(2, –1)
D)
no solution
Provide an appropriate response.
127)
Given matrix A:
A = 5 7 – 6
–4 9 1
What is the size of A?
127)
A)
3 × 2
B)
2 × 3
C)
3
D)
3 × 3
Solve the system of equations by graphing.
128)
y=x + 1
y=3x – 5
128)
A)
(4, 3)
B)
(–3, -4)
C)
(3, 4)
D)
no solution
Answer Key
Testname: C4
37
Answer Key
Testname: C4
Answer Key
Testname: C4
Answer Key
Testname: C4