Download Exam 1Review Solve the system of equations. 1) x + 5y = 2 2x + 6y

Exam 1Review
Solve the system of equations.
1) x + 5y = 2
2x + 6y = 4
2) -7x + 5y = 14
3x + 3y = -6
3) 4x - 2y = 6
20x - 10y = 24
4) 2x + 6y = 4
10x + 30y = 20
5)
7x 5y
+
=4
3
4
5x
- 2y = 21
6
Use the indicated row operation to change the matrix.
1
1
6) Replace R2 by R1 + R2 .
2
2
20 2
-2 2 10
7) Replace R2 by R1 + (-1)R2 .
1 -3 4
2 31
Solve the system of equations.
8) 3x + y + z = 5
4x + 5y - z = -8
10x + 7y + z = 2
9) x + 3y + 2z = 11
4y + 9z = -12
x + 7y + 11z = - 1
10) x - y + z = 8
x+y+ z=6
3x + y + 3z = 10
11) x - y + 8z = -107
x + 2y
= 21
2x + y + 8z = -80
12) 9x + 9y - z = 99
x - 6y + 6z = 38
-9x + y + z = -59
1
13) 2x - y - 5z = -39
-8x + 5y - 3z = -43
-2x - 9y + z = -77
14) 9w + 7x - 6y - 2z = 6
8w + 5x - 9y - 2z = -15
9w - 7x + 7y + 3z = -22
-6w - 2x + 7y + 9z = 6
Solve the problem.
15) 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.
16) Jane wants to buy a photocopier. The salesperson has the following information on three models. If all three are
used, a specific job is completed in 50 minutes. If copier A operates for 20 minutes and copier B operates for 50
minutes, one-half of the job is completed. If copier B operates for 30 minutes and copier C operates for 80
minutes, three-fifths of the job is completed. Which is the fastest copier, and how long does it take this copier to
complete the entire job working alone?
17) Janet is planning to visit Arizona, New Mexico, and California on a 16-day vacation. If she plans to spend as
much time in New Mexico as she does in the other two states combined, how can she allot her time in the three
states? (Let x denote the number of days in Arizona, y the number of days in New Mexico, and z the number of
days in California. Let z be the parameter.)
Find the values of the variables in the equation.
18) 6 -5 x = m -5 3
n 8 p
-4 y -3
19) -3x y + 2
7z
5
6
0
+ 8x -4 7
1 2 3m
= 5 8 7a
3 7 0
Perform the indicated operation, where possible.
20) -4 1 + 6 2
25
6 -3
21) 4 4
+ 1
5
Find the value.
22) Let A = 2 3
26
and B =
1
23) Let C = -3
2
and D =
0 4 ; 3A + B
-1 6
-1
3 ; C - 2D
-2
2
Perform the indicated operation, where possible.
21
-1 4
24) 0 4 - 7 4
6 -4
42
Find the matrix product, if possible.
25) -1 3 0 -2 7
32
1 -3 2
30
-3 1
04
26) 1 3 -3
3 0 4
27) 0 -2
4 3
3 2 -2
2 -3 7
28) 3 -2 1
0 4 -2
+ -4 1 4
-2 2 -6
30
-2 2
Solve the problem.
29) A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount of
ingredients in one batch. Matrix B gives the costs of ingredients from suppliers X and Y. Multiply the matrices.
sugar choc
4
6
5
3
3
3
A=
B=
X
3
3
2
Y
2
4
2
milk
1
1
1
cherry
almond
raisin
sugar
choc
milk
Find the inverse, if it exists, for the matrix.
30) 0 5
-5 -5
31) -5 -2
-7 8
32)
2 -1 0
3 -2 0
-2 3 1
Solve the system of equations by using the inverse of the coefficient matrix.
33) x + y + z = -9
x - y + 4z = -8
5x + y + z = -13
3
34) 3x - 4y - 7z = -50
-5x + 5y + 5z = 35
-9x - 2y - 9z = -100
Solve the matrix equation AX = B for X by finding A-1 , given A and B as follows. Use a graphing calculator to obtain your
answer, rounding all numbers to four decimal places.
2 -1
3
6
35) A = -3 4 -5 , B = 2
6
-4 0
-4
Find the production matrix for the input-output and demand matrices using the open model.
36) A = 0.25 0.08 , D = 500
0.33 0.11
600
Find the ratios of products A, B, and C using a closed model.
A B C
37)
A 0.2 0.3 0.1
B 0.3 0.1 0.8
C 0.5 0.6 0.1
Solve the problem.
38) Suppose the following matrix represents the input-output matrix of a simplified economy that involves just
three commodity categories: manufacturing, agriculture, and transportation. How many units of each
commodity should be produced to satisfy a demand of 900 units for each commodity?
Mfg Agri Trans
Mfg 0 1/4 1/3
Agri 1/2 0 1/4
Trans 1/4 1/4 0
39) The input-output matrix for an economy is given below.
Agri.
Agri. 0.04
Mfg. 0.02
Mfg.
0.18
0.22
The demand matrix is
D=
700
1000
Find the amount of each commodity that should be produced.
40) A simplified economy is based on agriculture, manufacturing, and transportation. Each unit of agricultural
output requires 0.3 unit of its own output, 0.5 of manufacturing, and 0.2 unit of transportation output. Each unit
of manufacturing output requires 0.3 unit of its own output, 0.1 of agricultural, and 0.4 unit of transportation
output. Each unit of transportation output requires 0.4 unit of its own output, 0.2 of agricultural, and 0.1 of
manufacturing output. There is demand for 35 units of agricultural, 90 units of manufacturing, and 10 units of
transportation output. How many units should each segment of the economy produce?
4
Answer Key
Testname: EXAM 1 REVIEW
1)
2)
3)
4)
5)
(2, 0)
(-2, 0)
No solution
- 3y + 2, y
(6, -8)
6) 2 0 2
016
7) 1 -3 4
-1 -6 3
-6z + 33 7z - 44
,
,z
8)
11
11
9)
19z + 80 -9z - 12
,
,z
4
4
10)
11)
12)
13)
14)
15)
16)
17)
18)
No solution
No solution
(8, 4, 9)
(7, 8, 9)
(-1, 5, 4, -2)
$10,000 at 5%, $5000 at 6%, and $10,000 at 8%
A is fastest; 120 minutes
x = 8 - z, y = 8, 0 z 8
m = 6, x = 3, n = -4, y = 8, p = -3
13
2
,z= ,m=0
19) x = 1, y = 10, a =
7
7
20) 2 3
82
21) Not possible
22) 6 13
5 24
3
23) -9
6
-3 3
24) -7 0
2 -6
3
-7 -1
25)
2 -12 25
26) -6 -9
9 16
27) 0 2 -2
-4 9 11
28) Does not exist
29)
X Y
32 34 cherry
26 24 almond
20 20 raisin
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Answer Key
Testname: EXAM 1 REVIEW
30)
-
1 1
5 5
1
5
0
31) No inverse
32)
2 -1 0
3 -2 0
-5 4 1
33) (-1, -5, -3)
34) (4, 5, 6)
3.1724
35) 4.6897
1.4483
36)
769
959
37) 33: 67: 63
38) 2241 units of manufacturing, 2538 units of agriculture, and 2097 units of transportation
39) 974.2 units of agriculture and 1307.0 units of manufacturing
40) Agriculture: 274; manufacturing: 257; transportation: 150
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