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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