Name__________________________________ Date____________ Block_________
Algebra 2
Ch. 4 Test Review
Use the following matrices to perform the given operations.
3 4 
 3 1 
 1 2
5 1 


A  6 -2 B   2 4 C  
D

3 1 
0 2


1 0 
 1 5 
1. 4B – 3A
2. 5C – D
3. 2AC
4. CA
 2 0  1 4 2 
5. Explain why the problem 

 is not possible.
1 2  0 12 9 
Give the dimensions of each matrix and identify the indicated element.
4 5 0
 11 3 1
6.  2 1 9 12 0 1 , a21
7. 
 8 5 13

 5 3 0
9 1 
1 0 
, a34
21 35

0 0
8. Is matrix multiplication commutative? Explain why or why not?
Find the missing dimensions. If not possible, write “Not Defined”.
9. A2x3 • B3x2 = C__
10. A3x2 • B__ = C3x1
11. A2x3 • B2x3 = C__
Name__________________________________ Date____________ Block_________
Algebra 2
6 4 1   9 0 
12. Is the problem 

 possible? Explain why or why not?
0 0 6   4 1 
13. The following table displays
data from a study conducted by a
school.
a. Write a matrix H to represent the data in the table below.
b. Find element h23. What does this element represent?
14. A florist creates three special floral arrangements. One uses three lilies. The second
uses three lilies and four carnations. The third uses four daisies and three carnations.
Lilies cost $2.15 each, carnations cost $0.90 each, and daisies cost $1.30 each.
a. Write a matrix to represent the number of each type of flower in each arrangement.
b. Write a matrix to represent the cost of each type of flower.
c. Find the matrix representing the cost of each floral arrangement.
Find the determinants of each matrix if they exist.
15.
1
8
2
7
1 5 2
16. 0 7 1
2 4 3
17.
1
2
1
5 3 0
Name__________________________________ Date____________ Block_________
Algebra 2
Solve for each variable.
18. 3 2 x 3 3z   12 3 y 9
3   4 9 
2 x 1  0
19. 




 2 0 2 x  y   0 6 
Find the inverse of each matrix. If it does not exist, explain why not?
 3 1
3 6
20. 
21.

4 8
 4 5 


22. If matrix A and matrix B are inverses of each other, what is the resulting matrix when they are
multiplied together?
23. Solve.
 2 0
 10 5 
3

2
X


 0 17 
 1 5 


Write the matrix equation and solve. Show all steps.
24.
7x  5y  3
3 x  2 y  22
25.
y  3x  7
x2
Name__________________________________ Date____________ Block_________
Algebra 2
26. What happens when you multiply a matrix by the identity matrix?
27. Replace the variable matrix with a numerical matrix that will make the statement true.
 1 9  a b   1 9 
12 5  c d   12 5


 

28. Do all matrices have inverses? Explain why or why not.
29. Solve the system using the calculator. Show each step.
 2w  x  y  2
  w  2 x  y  z  4


2 w  3 x  3 y  2 z  2
 w  x  2 y  z  6
30. Explain what it means for a system to have a unique solution.