Name __________________________________
Algebra 2 - Chapter 4 Quiz Review
1. Use the table for Exercises a and b.
Construction
Manufacturing
Transportation
Sales
Finance
Services
Government
a. What are the dimensions of the matrix?
b. Identify
A21 and tell what it represents.
June, 1992
17.6%
8.3%
5.4%
8.7%
4.0%
6.6%
3.5%
Find each sum or difference.
2.
4.
 4 7  9 3
  2 1    6 0

 

3.
Find the product. Show your work.
 4  5 1   7  10 4
10 7
4    17
0 3

21  9  6  2  6 1
2 6  1 5
1 0   3 1



Solve each matrix equation.
5.
 3  8
 2 8
10 5   X   1 12




7.
Find the values for x and z..
8.
Solve for X.
6.
 2 0  5 10
2X  


 1 4  15 9 
 13 2 x  1
 4x 
5 1  2
0 2   10  10   5 z
2.5 z  x 

 
 
 3 2
 10  11
 1 5 X   26  36




June, 1996
9.5%
5.1%
4.5%
6.4%
2.6%
5.1%
2.7%
9. Find the dimensions of the product matrix. Then find each product..
1 2   2 1 
a. 


 2 1  1 2 
1 
 
b. 2 1 2 3 4
 
3
c.
 8 5  1
2

0 9 7
10. Use an inverse matrix to solve each equation or system.
a.
3 5 
 2 6 
6 2 X   4 12




b.
x  y  3

2 x  y  1
Find the inverse of each matrix if it exists. If it does not exist, write no inverse.
11. a.
4 7 
E

3 5
b.
J=
3 4
3 4


Solve each system using inverse matrices. Show your work.
12.
 x  y  z  31

a.  x  y  z  1
x  2 y  2z  7

b.
 3 x  4 y  2

 x  y  1
13. Explain how to determine whether two matrices can be multiplied and what the dimensions of the product matrix will be.
14. Are these matrices inverses of each other? Show why or why not.
a.
 3 2  3  2
 4 3 ,   4 3 

 

b.
  3  7   5  7
 2 5 ,  2 3 

 

15. An apartment building has 50 units. All are one- or two- bedroom units. One-bedroom units rent for $425/mo, and twobedroom units rent for $550/mo. When all units are occupied, the total monthly income is $25,000. How many apartments
of each type are there?
Algebra 2
Answers Review Chapter 4
1a. 7x2
1b. Manufacturing 8.3%
 13 4
2. 

 8 1 
 3  15 5 
 27
3.
7
7 

 19  15  5
 1  16
11  7 


4.
16 16
 1 5 


5.
6.
1.5 5 
 7 6.5


7. x = 3; z = -2
 6 1 
 4  7


4 5
9a. 2 x 2 

5 4
8.
1 2 3 4 


9 b. 3 x 4 2 4 6 8


3 6 9 12
9c. 2 x 3
 16 10  2
 0 18 14 


 1 2
 1 0



5
7


11a. 

 3  4
10a.
12a. (-5, 15, 21)
10b. (-4, -7)
11b. no inverse
13b. (-2, -1)
13. Answers will vary
14a. yes
15b. no
15. 20 one-bedroom, 30 two-bedroom
What You’ll Need to Know Today:
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
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


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How to find the dimensions of a matrix
How to find an element in a matrix
How to add/subtract matrices
How to determine if two matrices are inverses of each other
o How to multiply matrices by hand (only have to do one)
How to multiply a matrix by a scalar
How to find the inverse of a matrix using your calculator
How to solve a matrix equation
How to solve a system of equations with inverse matrices (on
your calculator)
How to make a system of equations from a word problem
o Then solve using inverse matrices (on your calculator)
Finding values for x and y using equal matrices