Accelerated Pre-Calculus
REVIEW: Matrices
Name _________________________________
NO CALCULATOR!!
___ 1. Which of the following matrices has an inverse?
4 8
A. 

2 4
B. 1
C. 3 5 1
3 4
D. 

4 6
2. Solve the following system of equations using inverse matrices:
5 x  2 y  1
. ___________

 x  4 y  35
___ 3. Solve:
2y y
5
A. y = -1, 1
y
 2
B. y = -1
C. y = - ½, -2
10 5
4. Find A1 if A  
. (Circle your final answer.)
2 
7
a 0
1
5. If A  
 , find A . Simplify. (Circle your final answer.)
0
b


D. y = -2
6. What would make a matrix have an inverse that does not exist?
7. What are the dimensions of matrix M if M  A14  B24 ? __________________
 1 3
D   1 2 
 2 3 
Evaluate. If not possible, state why. (Circle your final answer.)
 2 1 3 
8. Let A  

 0 1 2 
a) 2C  B
 4 2 
B

 1 1
 2 3
C

 1 4
b) AB + C
c) C 1
9. What is the area of the triangle in square units with the given vertices?
(Circle your final answer.)
 -3, 4 
 6,3 
 2,- 1
10. Identity Matrix: Know properties of identity matrix (section 1.11). (e.g. what do you
multiply to get the identity matrix as your answer, what do you get if multiply by
identity matrix, etc…)
2 1 5
11. What is the determinant of  3 1 2  ? (Circle your final answer.)
 0 4 2 
 x  2  5  7 
12. Find x and y: 2 
       (Circle your final answer.)
 y  3  4 1 
 2 1  16 8 
13. Find x and y: 2x 
(Circle your final answer.)

40 
 10 5   y
14. Matrix Properties: Review the properties of matrix worksheet. Which ones work,
which ones don’t, etc…
15. Vertex-Edge Graph: See section 1.12—Be able to draw vertex-edge graph, write a
matrix from the graph, and then answer questions based on the graph/matrix.
CALCULATOR
___#16-17. System of Equations: See #17 below (Question about Shaq)
18. Use a graphing calculator to find the determinant of the matrix. (Circle your final
answer.)
19. Use
0
2

 0
a graphing calculator to find the inverse of the matrix. (Circle your final answer.)
1
0
1  2 
2
2 
20. Solve the following system using a graphing calculator. (Circle your final answer.)
4x + 5y + z = 4
5x - 3y - 1z = - 7
4x - 3y + 2z = 2