Name _Answer Key________________
Math III
Unit 1 Review (Matrices)
**Identify the standard that each problem addresses. This will help reinforce what standards will
be covered on the test and aid in the mastery of these standards. ***
1. What is the order of the following matrix?
5 2 10 
 1 0 3 


Answer: 2x3
2. Perform the indicated matrix operation, if possible.
 4 2  7
Answer: 10 9
4 

 3 12 2 
3. Perform the indicated matrix operation, if possible.
10 5  25

30  15 20 
Answer: 
4. Use matrices A and B to evaluate the 2A + B.
10  6  2 7 8 1



14 4    5 1 9 5
Answer: 
5. Derek asked the students in two history classes how many students went to a movie, went to a concert,
or went shopping last weekend. He recorded the results in two matrices.
Find the total for the two classes.
M
C
S
M
Males
Males
Females
Females
 4 9 8

10 15 4
Answer: 
C
S
6. A company stocks items A, B, and C at each of its two stores. Use matrix multiplication to determine
the value of the inventory at each store.
Answer:
store1 600
store2 433
7. Evaluate the determinant
2 1
2 6
Answer: determinant = 12-(-2) = 14
8. Find the inverse of the matrix.
Answer:
9. Are the matrices
and
1  2  2   1  1


4   5 2 2 
2  5
inverses? Explain why or why not.
1  3 4 0 1 0



0 2  1 1 0 1
Answer: No, they are not inverses of each other. 
10. A real estate agent is writing a listing for a triangular piece of land. She has to include the number of
square feet for the property and has to calculate it from a plot that shows the following information: one
corner of the plot is 132 feet south and 140 feet east from the upper vertex of the plot, the other corner is
20 feet south and 268 feet east from the upper vertex of the plot. Use matrices to find the area of the piece
of land.
Answer:
Points (0,0), (140, -132), (268, -20)
0
1
 0
1
1
1
A   140  132 1   0  0  (2800)   (35376)  0  0  32576  16288 ft 2
2
2
2
268  20 1
11. Which of the following can be used to represent a system of linear equations?
Write an augmented matrix for the system of linear equations.
4x 
2x
y
 1
y  2z  0
 5 z  2 Answer:
4 1 0   x   1 
0 1  2   y    0 

    
2 0  5  z   2
12. Sunshine Coffee Company wants to mix Guatemalan Gold coffee that costs $12 a pound with
Ethiopian Bold coffee that costs $8.50 a pound to get 40 pounds of House Blend that costs $9.90 a pound.
a. Using x for the amount of Guatemalan Gold coffee used and y for the amount of Ethiopian Bold coffee
used, write a system of equations that models this situation. Then write a matrix equation for the system
and solve.
Answer:
x  y  40
12 x  8.50 y  396
1   x   40 
1
   

12 8.50  y  396
Matrix Equation: 
Solution: (16 pounds GG, 24 pounds EB)
13. Use an inverse matrix to solve the linear system.
Answer: B
Which of the following shows the correct solution?
A.
C.
B.
D.
14. Use an inverse matrix to solve the linear system.
4  1  x  20
       Solution (4, -4)
6 6   y   0 
Answer: 
****OMIT problems 15-20****
21. An airline serves four cities: Asheville, Bedford, Grantsville, and Hanover. There are flights between
Asheville and Grantville, Asheville and Hanover, Bedford and Grantville, and Bedford and Hanover.
Draw a vertex-edge graph to represent this situation and then construct a matrix to represent the vertexedge graph.
Asheville
Answer:
Bedford
Grantville
A B G H
Hanover
A 0
B 0
Matrix:
G 1

H 1
0 1 1
0 1 1
1 0 0

1 0 0