Provide an appropriate response.
151)
A manufacturer who produces one product is only interested in tracking material costs.
What is the order of the matrix he would use?
151)
Set up a matrix equation with integer values that is equivalent to the system of equations.
152)
y=1
2x–3
10
y= – 3x+13
2
152)
Provide an appropriate response.
153)
Find the inverse matrix of
1–2 0
2 1 2
0 0 –1
.
153)
154)
If A=
5–2
–4 3
1 4
and B=
7 5 0
–2 1 1
1–3–5
, find BA.
154)
155)
Let A=
1 2 3
2 5 7
–3–6–10
. Find A–1.
155)
156)
Solve by the method of reduction:
x + 2y– 3z= 4
2x – 3y– 5z= – 1
–3x + 8y– 13z= 4
156)
38
157)
Solve by the method of reduction:
x + 2y– 5z= 1
3x – 4y– 11z= 6
–2x– 6y– 16z= – 5
157)
158)
Perform the indicated operations and simplify your answer: 2 –31
6
158)
Use the encoding matrix E =1 3
2 4 , an additional coding matrix, F =
–23
2
1–1
2
, plus the matrices I =1 0
0 1 and O =0 0
0 0
to answer the question.
159)
I–E
159)
Provide an appropriate response.
160)
Solve the matrix equation: x y +2
x+y4
=x1
0 4
160)
Secret messages can be encoded by using a code and an encoding matrix. If we have the code:
a b c d e f g h i j
1 2 3 4 5 6 7 8 9 10
k l m n o p q r s t
11 12 13 14 15 16 17 18 19 20
u v w x y z space
21 22 23 24 25 26 27 and an encoding matrix E, we can encode a
message by taking every two letters of the message, converting them to their corresponding numbers, creating a 2 × 1
matrix, and then multiplying each two numbers by E. The message may be unscrambled with a decoding matrix which is
the inverse of the coding matrix, E–1. Determine if the given pair of encoding matrices are inverses of each other.
161)
1 2
3 4 and –2 1
1.5 –0.5
161)
1 2
39
A zoo veterinarian can purchase animal food of 4 different types, A, B, C, and D. Each food comes in the same size bag,
and the number of grams of each of three nutrients in each bag are summarized in the following table. Use this
information to answer the questions that follow.
Food
A B C D
N15 5 10 5
Nutrient: N210 5 30 10
N3515 10 25
162)
For one animal, she determines that she needs to combine these bags to get 15,000 g of N1,
30,000 g of N2, and 19,000 g of N3. How many bags of each type of food should she order?
162)
Provide an appropriate response.
163)
By using matrix reduction, solve the system:
x1+2x2–3x3+ x4=1
2x1+x2+2x4=8
163)
If E =1 3
2 4 is the encoding matrix, compute the following.
164)
E2
164)
Provide an appropriate response.
165)
Use matrix multiplication to represent the system: 3x+ 2y=2
165)
If E =1 3
2 4 is the encoding matrix, compute the following.
166)
E5(Use the matrix operations on a graphing calculator.)
166)
40
167)
A courier service has an order to deliver four products to a factory. The table below gives
the specifications of the products.
A B C D
Volume(ft3) 5 2 9 17
Weight(lb) 20 10 40 70
Value($) 300 200 700 1100
If the company’s large van can carry 500 cu ft.; 2100 lb, and is insured for $34,000, how
many units of each product can be carried? Write the answer in terms of A, B, C, and D.
167)
Secret messages can be encoded by using a code and an encoding matrix. If we have the code:
a b c d e f g h i j
1 2 3 4 5 6 7 8 9 10
k l m n o p q r s t
11 12 13 14 15 16 17 18 19 20
u v w x y z space
21 22 23 24 25 26 27
and an encoding matrix: E =1 3
2 4 , we can encode a message by taking every two letters of the message, converting them
to their corresponding numbers, creating a 2 × 1 matrix, and then multiplying each two numbers by E. Use the code and
encoding scheme above and an additional encoding matrix, F =5 7
6 8 , to answer the question.
168)
If the letters to be encoded are L=i
t, show that E(FL) = (EF)L.
168)
Let matrix A represent the sales (in thousands of dollars) of a toy company in 1994 in three cities, let B represent the sales
in the same cities in 1995, and let C represent the sales in the same cities in 1996.
Action
Educational A =400 350 150
450 280 850 ; B =410 300 200
375 300 710 ; C =380 330 220
460 320 750
169)
What is the change in sales between 1994 and 1995?
169)
Provide an appropriate response.
170)
Using the method of reduction, solve the system:
3x–2y+z= – 1
2x–y–z=5
2x+3z=4
170)
41
Provide an appropriate response.
171)
An economy is based on two sectors, agriculture and manufacturing. Production of a dollar’s worth
of agriculture requires an input of $0.40 from agriculture and $0.10 from manufacturing.
Production of a dollar’s worth of manufacturing requires an input of $0.20 from agriculture and
$0.30 from manufacturing. Find the output for each sector that is needed to satisfy a final demand
of $16 billion for agriculture and $32 billion for manufacturing.
171)
A)
$44 billion agriculture, $52 billion manufacturing
B)
$52 billion agriculture, $44 billion manufacturing
C)
$36 billion agriculture, $56 billion manufacturing
D)
$56 billion agriculture, $36 billion manufacturing
172)
Given the coefficient matrix A and the final demand matrix D stated below, find (I – A)–1 and find
the output matrix X.
A =0.3 0.3
0.2 0.2 C =70
30
172)
A)
(I – A)–1=0.6 1.6
0.4 1.4 ; X =130
70
B)
(I – A)–1=1.6 0.6
0.4 1.4 ; X =70
130
C)
(I – A)–1=0.6 1.6
0.4 1.4 ; X =70
130
D)
(I – A)–1=1.6 0.6
0.4 1.4 ; X =130
70
173)
A large oil company produces three grades of gasoline: regular, unleaded, and super–unleaded. To
produce these gasolines, equipment is used which requires as input certain amounts of each of the
three grades of gasoline. To produce a dollar’s worth of regular requires inputs of $0.14 worth of
regular, $0.18 worth of unleaded, and $0.17 worth of super–unleaded. To produce a dollar’s worth
of unleaded requires inputs of $0.14 worth of regular, $0.15 worth of unleaded, and $0.13 worth of
super–unleaded. To produce a dollar’s worth of super–unleaded requires inputs of $0.15 worth of
regular, $0.17 worth of unleaded, and $0.11 worth of super–unleaded. In addition, the oil company
has final demands for each of the different grades of gasoline. Find the coefficient matrix that
would be used in determining the total output of each grade of gasoline.
173)
A)
A =
0.14 0.14 0.15
0.18 0.15 0.17
0.17 0.13 0.11
B)
A =
0.14 0.18 0.17
0.14 0.15 0.13
0.15 0.17 0.11
C)
A =
0.13 0.18 0.17
0.16 0.15 0.13
0.15 0.17 0.11
D)
A =
0.13 0.16 0.17
0.14 0.15 0.13
0.15 0.17 0.11
44
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