Algebra 2
Review Chapter 4
Name __________________________________
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

 

Find the product.
3.
 4  5 1   7  10 4
10 7
4    17
0 3

21  9  6  2  6 1
6.
 2 0  5 10
2X  


 1 4  15 9 
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.
 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




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
June, 1996
9.5%
5.1%
4.5%
6.4%
2.6%
5.1%
2.7%
10. Use an inverse matrix to solve each equation or system.
a.
3 5 
 2 6 
X

6 2 
 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


Find the determinant of each matrix.
12. a.
8  3
2 9 


b.
0.5  1
3
0 

Solve each system. Show your work.
13.
 x  y  z  31

a.  x  y  z  1
x  2 y  2z  7

b.
 3 x  4 y  2

 x  y  1
14. Explain how to determine whether two matrices can be multiplied and what the dimensions of the product matrix will be.
15. Are these matrices inverses of each other?
a.
 3 2  3  2
 4 3 ,   4 3 

 

b.
  3  7   5  7
 2 5 ,  2 3 

 

16. 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.
10b. (-4, -7)
11b. no inverse
12a. 78
12b. 3
13a. (-5, 15, 21)
13b. (-2, -1)
14. Answers will vary
15a. yes
15b. no
16. 20 one-bedroom, 30 two-bedroom