Name______________________________
Algebra 2 – Test Chapter 4
Class______________Date_________
1. The table shows record high and low temperatures in degrees Fahrenheit in each of six cities.
City
Record High Record Low
Anchorage
85
-34
Chicago
104
-27
Houston
107
7
Miami
98
30
Pittsburgh
103
-18
San Diego
111
29
a) Display the data in matrix whose rows indicates the data for each city.
b) What are the dimensions of the Matrix? __________
c) Identify a 42 __________
Find each sum or difference.
#2.
9 2  7  5
8  1  6 3 

 

#3.
 1 13 16  22 7  18
24  3 19    5 15 11 

 

 9 10 20 12 14  17
Find each product if possible. If not possible, write product undefined.
 9 15 6
 3 10 
  8 2 7   2 4 0
 3
#4.
#5.


  5 0 8
21  4

 63  8 1 
Name______________________________
Class______________Date_________
6.  ABC has coordinates (1,1), (3,4), and (0,-5)
a. Write the vertices in matrix form.
b. Find the coordinates of the image of the triangle after a Translation right 3 units and up 2 units
c. Find the coordinates of the image of the triangle after a 270° Rotation
d. Find the coordinates of the image of the triangle after a Reflection in the line y = x.
Find the determinant of each matrix.
 6  7 
#7.
5
8 

#8.
 1  5
 2 9 


Find the inverse of each matrix if it exists. If it does not exist, write no inverse.
8 
6 2 
 7
#9.
#10.
3 2
 14  16




Solve each matrix equation.
#11.
3 4
 3
X

 1  1
 2


 
#12.
 1 3 6  8 1 0 
X 


 1 2 1 14 3  1
Name______________________________
Class______________Date_________
Solve each matrix equation.
  3  2
8  1
#13. 
X 


1
1
6 0 
#14.
3 2  10 8 
4X  3


1  2  5  2
Solve the following systems using inverse matrices. Show your work.
2 x  3 y  4 z  3
2 x  y  2

15.
16.

 13x  5 y  2 z  3
2 x  2 y  4
 3 x  4 y  3 z  6

 1 0 
A= 

 3  4
  3 3
B= 

 5 0
17. Show that AB and BA are not Equal
Name______________________________
Class______________Date_________
18. Are these matrices inverses of each other? Show why or why not.
 2  1
  1  1
 3 1  and  3  2




19. What are the dimensions of the product of a 2 X 3 matrix and a 3 X 4 matrix?
20. You bought ten carnations and five daisies for a total of $12.50. Later that day you bought five
carnations and eight daisies for a total of $11.75. Find the price of each carnation and of each daisy.
Extra Credit:
Emily was taking her large pet rabbit, a basket of prize winning baby carrots, and her small, but hungry, rabbit-chasing
dog to town. She came to a river and realized that she had a problem. The little boat she found tied to the pier was only
big enough to carry herself and one of three possessions. She couldn’t leave her dog on the bank with her little rabbit
(the dog would frighten the poor rabbit) and she couldn’t leave the rabbit alone with the carrots (the rabbit would eat all
the carrots). She had to figure out how to cross the river safely with one possession at a time while insuring that the dog
and rabbit were not left together, and that the rabbit and carrots were not left together during the crossing. How could
she safely move back and forth across the river to get her three possessions to the other side?