College Algebra
Chapter 10 Test
Name: ______________________________
Question 0 (1 point): What are your summer plans??  _____________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
Simplify.
3
6
0 −1
1. [−1 −3] + [6 0 ]
−5 −1
2 3
5
3. −5 [
4
2. [
−5 2 −2
6 −5 −6
]−[
]
4 −2 0
1 3 −3
6 −4
]
−2 −1
Simplify. Show all work, then check your answer using your calculator.
−2
−5 −5
4. [
]∗[
3
−1 2
−3
]
5
−4 2
5 3 5
5. [
] ∗ [−3 4 ]
1 5 0
3 −5
For 6 & 7 solve the systems using elimination and/or substitution:
6.
– 𝑥 − 5𝑦 − 5𝑧 = 2
4𝑥 − 5𝑦 + 4𝑧 = 19
𝑥 + 5𝑦 − 𝑧 = −20
7.
4𝑥 − 𝑦 + 6𝑧 = 27
−4𝑥 − 2𝑦 + 3𝑧 = 21
4𝑥 − 6𝑦 + 2𝑧 = 12
Solve the following system using row reduced echelon form.
8.
6𝑥 − 6𝑦 − 4𝑧 = −10
−5𝑥 + 4𝑦 − 𝑧 = −12
2𝑥 + 3𝑦 − 2𝑧 = 9
𝑅2 = 5𝑟1 + 𝑟2
𝑅3 = −2𝑟1 + 𝑟3
[
[
|
[
Matrix
|
]𝑅
3
1
=
𝑟
134 3
]
[
|
𝑅2 = 𝑟3 + 𝑟2
|
]𝑅
1
[
= 𝑟2 + 𝑟1
|
[
]
|
𝑅1 = 2𝑟2 + 𝑟1
𝑅3 = −7𝑟2 + 𝑟3
]𝑅1 = 41𝑟3 + 𝑟1 [
|
𝑅2 = 18𝑟3 + 𝑟2
Solution: ___________________
Solve the following system using any method (no work required )
9.
5𝑥 + 𝑦 − 4𝑧 = −4
−3𝑦 − 6𝑧 = −21
−𝑥 − 𝑦 − 𝑧 = −6
Solution: ______________________
]
10.
−2𝑥 − 5𝑦 + 4𝑧 = 21
−5𝑥 − 5𝑦 + 𝑧 = 21
−4𝑦 − 4𝑧 = 8
Solution: ______________________
]
11. Use the system of constraints to maximize the objective function z = 2x + 4y.
𝒙+𝒚 ≤ 𝟔
{ 𝒙≥𝟐
𝒚≥𝟎
1
1
12. A factory manufactures two types of ice skates: racing skates and figure skates. The racing skates require 6
work hours in the fabrication department, whereas the figure skates require 4 work hours there. The racing
skates require 1 work-hour in the finishing department, whereas the figure skates require 2 work hours there.
The fabricating department has available at most 120 work hours per day, and the finishing department has no
more than 40 work hours per day available. If the profit on each racing skate is $10 and the profit on each figure
skate is $12, how many of each should be manufactured each day to maximize profit?
5
5
13. A factory produces gasoline engines and diesel engines. Each week the factory is obligated to deliver at
least 20 gasoline engines and at least 15 diesel engines. Due to physical limitations, however, the factory cannot
make more than 60 gasoline engines nor more than 40 diesel engines in any given week. Finally, to prevent
layoffs, a total of at least 50 engines must be produced. If gasoline engines cost $450 each to produce and diesel
engines cost $550 each to produce, how many of each should be produced per week to minimize the cost?
5
5