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Accelerated Precalculus
1.7 Matrices Test Review
Name________________________
You are responsible for reviewing ALL notes, class work and homework from this unit! You
should be able to perform everything by hand and on the calculator except for finding the
inverse of a 3x3 matrix.
 1 4 1
D   2 5 2 
 7 5 4 
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 6 4 
Given: A  

 2 3 
k 0 
B

 1 4 
1. What are the dimensions of C?
 1 1 k 
C

3 4 5 
2. What element is found at C2,1 ?
3. What are the dimensions of matrix M if X2x5 M  Y2x 6 ?
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Perform the following operations:
4. 3A – 2B
5. BC
6. det (A)
7. A1
8.
D
9. D1
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Solve the matrix equation for the unknowns.
4 1
1 3x 2 
 x  2 0
 16 3
11. 
 2 0   
  3

2
3 0 5 0 1   6 2
 2


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 x 7 2 10
10. 
    
 3 y  5  1 
Solve for x.
Given the matrix below, what value of x will
make A1 impossible to find and why?
12 4 6
12. 2
x
x 3  6x  4
0 2
 5 6 
13. A  

 3  x 
14. Use matrices to write the equation of the parabola that passes through the points (4, 6),
(2, -12) and (-1, 21).
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Write the matrix equation that represents the system, and solve the system by using the
matrix equation.
3 x  y  3
15. 
6 x  12y  6
(No calculator)
 x  y  16

16.  x  z  4
(Use a calculator)
2y  3z  4

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1 4 
1 3
17. If A  
and B  
and X  A1  B1 , find X2,2 .


2 1 
3 2 
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Write a system of equations for the following situation and solve using a matrix equation.
18. You have $33 to spend on 24 balloons. Birthday balloons cost $1.50 each,
congratulations balloons cost $1.00 each, and get well balloons cost $2.00 each. You want
twice as many birthday balloons as the other two types combined. Calculate how many of
each you should buy.
19. A company manufactures 3 types of home theater systems: a 300-watt system, an 800watt system, and a 1000-watt system. The systems are shipped to two warehouses. The
numbers of units shipped to each warehouse this month and last month are given below:
This month (A)
Last month (B)
300W 800W 1000W
300W 800W 1000W
Warehouse 1
Warehouse 2
3500 7850 7220
2980 8310 7450


3670 7350 7490
3190 8050 7160


a. Write a matrix M that gives the total number of each type of home theater system
shipped to the each of the two warehouses for the two months.
b. Write a matrix N that gives the difference of the number of units shipped this month
and the number of units shipped last month.
c. How would you determine the average number of units shipped to each warehouse for
the two months? Find the matrix that represents the average number of units
shipped.
d. If the 300-watt system sells for $149.99, the 800-watt sells for $249.99 and the
1000-watt system sells for $399.99, how much money did the company make this
month at each warehouse?
e. If the 300-watt system costs the company $49.99 to manufacture, the 800-watt
system costs $99.99 to manufacture and the 1000-watt system costs $199.99 to
manufacture, how much profit did the company actually make at each warehouse?
*Be sure that you also review the “mixture” problems from the systems worksheet*
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20. A ferry system has routes between ports A and B, B and C, B and D, C and D, and A, and
D.
a. Draw a vertex-edge graph to represent this situation.
b. Write a matrix M that represents the vertex-edge graph of this situation.
c. Calculate M2 and describe what this matrix represents.
d. Find the number of two-route trips there are from port B to port D.
21-22. Go back to the first page and find the additive identity for B and the multiplicative
inverse for A.