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Integrated V: World of Functions
Using Technology and Matrices with Systems
Name_________________________
Date: _____________ Period: ______
1. What are the four ways that we use to solve a system of equations:
_________________ _________________ ________________ _________________
2. Find each matrix product:
1 0  5
a. 
 
0 1 3 
6 2  1 0
b. 


0  3 0 1
1 0 
3. What do you notice about your answers? In what ways is the matrix 
 like the number 1?
 0 1
____________________________________________________________________________
4. Multiply the matrices below – use your calculator:
5 10  .3  1 
 .3  1  5 10
a. 
b. 





.5 3   .05 .5
 .05 .5 .5 3 
5. What do you notice about the answers? In what way is this pair of matrices like the pair of
numbers 3 and 1/3?
___________________________________________________________________________
 8 1 
6. Use your calculator to find the inverse of the matrix A= 
The inverse is written A-1

 6 2 
7. Multiply A and is inverse A-1. What did you get? _________________________________
8 10 
8. Find the inverse of the matrix C on your calculator if C = 
 . What did you find?
4 5 
Multiply the following:
 2  3  x 
9. 
 
 5 8   y 
3  2   x 
10. 
 
1 5   y 
3 2 5   x 
11.  1 0 7   y 

 
 2 4 1   z 
Rewrite the following as the product of two matrices:
12. 3x – 2y
-2x + 5y
13. x – y
2x + 7y
14. 2x – 3y + z
x + 2z
-2y + 4z
Now we are going to use inverses to solve systems of equations. Here is the system:
2x – 3y = 10
-5x + 8y = -26
Step One: Write the equation in Matrix form:



   
  
   
A
B
C



Step Two: Use your calculator to find the inverse of matrix A:



A-1
Step Three: Multiply Both sides of the matrix equation by the inverse:


  
 


 
 


  
 
A-1
A
B
A-1
C
1 0 
Step Four: When you multiply A-1*A, you will get 
 which is like 1 in regular multiplication, so
 0 1



 

 



Solve the following systems using matrices:
15. 2x + 3y = -16
4x +5y = 12
18.
-3w + x + 6y + 3z = 2
2w + z + 7y + 2x = 5
-3w -3 + x + 3z = -5y
3x = 2z = 6y = 6
16. .3x - .07y = 1.38
-.02x -.9y = .0037
17. x - 3y + 4z = 12
2x + y – z = -1
x + 2y + 2z = 3
19. 2x + y = 7
6x + 3y = 10