Integrated V: World of Functions Name_________
Using Technology and Matrices with Systems Date: ______Period: ______
1. What are the four ways that we use to solve a system of equations:
______
2. Find each matrix product:
a. b.
3. What do you notice about your answers? In what ways is the matrix like the number 1?
______
4. Multiply the matrices below – use your calculator:
a. b.
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?
______
6. Use your calculator to find the inverse of the matrix A= The inverse is written A-1
7. Multiply A and is inverse A-1. What did you get? ______
8. Find the inverse of the matrix C on your calculator if C = . What did you find?
Multiply the following:
9. 10. 11.
Rewrite the following as the product of two matrices:
12. 3x – 2y 13. x – y 14. 2x – 3y + z
-2x + 5y 2x + 7y 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
Step Four: When you multiply A-1*A, you will get which is like 1 in regular multiplication, so
Solve the following systems using matrices:
15. 2x + 3y = -16 16. .3x - .07y = 1.38 17. x - 3y + 4z = 12
4x +5y = 12 -.02x -.9y = .0037 2x + y – z = -1
x + 2y + 2z = 3
18. -3w + x + 6y + 3z = 2 19. 2x + y = 7
2w + z + 7y + 2x = 5 6x + 3y = 10
-3w -3 + x + 3z = -5y
3x = 2z = 6y = 6