Exam 1 Review
Exam 1 Review
Exam 1 Review
2) -7x + 5y = 14
3x + 3y = -6
3) 4x - 2y = 6
20x - 10y = 24
4) 2x + 6y = 4
10x + 30y = 20
7x 5y
5) + =4
3 4
5x
- 2y = 21
6
7) Replace R2 by R1 + (-1)R2 .
1 -3 4
2 31
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
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.)
19) -3x y + 2 6 + 8x -4 7 = 5 8 7a
7z 5 0 1 2 3m 3 7 0
21) 4 4 + 1
5
1 -1
23) Let C = -3 and D = 3 ; C - 2D
2 -2
2
Perform the indicated operation, where possible.
-1 4 21
24) 0 4 - 7 4
6 -4 42
30
26) 1 3 -3 -3 1
3 0 4
04
27) 0 -2 3 2 -2 + -4 1 4
4 3 2 -3 7 -2 2 -6
28) 3 -2 1 30
0 4 -2 -2 2
X Y
3 2 sugar
B= 3 4 choc
2 2 milk
31) -5 -2
-7 8
2 -1 0
32) 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
-4 0 6 -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
Agri. Mfg.
Agri. 0.04 0.18
Mfg. 0.02 0.22
D= 700
1000
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, 0)
2) (-2, 0)
3) No solution
4) - 3y + 2, y
5) (6, -8)
6) 2 0 2
016
7) 1 -3 4
-1 -6 3
-6z + 33 7z - 44
8) , ,z
11 11
19z + 80 -9z - 12
9) , ,z
4 4
10) No solution
11) No solution
12) (8, 4, 9)
13) (7, 8, 9)
14) (-1, 5, 4, -2)
15) $10,000 at 5%, $5000 at 6%, and $10,000 at 8%
16) A is fastest; 120 minutes
17) x = 8 - z, y = 8, 0 z 8
18) m = 6, x = 3, n = -4, y = 8, p = -3
13 2
19) x = 1, y = 10, a = ,z= ,m=0
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
25) 3 -7 -1
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
5
Answer Key
Testname: EXAM 1 REVIEW
30)
1 1
- -
5 5
1
0
5
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