1. Splash Screen

2. Concept

3. Example 1 Verify Inverse Matrices If X and Y are inverses, then X ● Y = Y ● X = I. Write an equation. A. Determine whether X and Y are inverses. Matrix multiplication

4. Example 1 Answer: Since X ● Y = Y ● X = I, X and Y are inverses. Write an equation. Matrix multiplication Verify Inverse Matrices

5. Example 1 Verify Inverse Matrices If P and Q are inverses, then P ● Q = Q ● P = I. Answer: Since P ● Q  I, they are not inverses. Write an equation. Matrix multiplication B. Determine whether P and Q are inverses.

6. Example 1 A.yes B.no C.not enough information D.sometimes A. Determine whether the matrices are inverses.

7. Example 1 A.yes B.no C.not enough information D.sometimes B. Determine whether the matrices are inverses.

8. Concept

9. Example 2 Find the Inverse of a Matrix Find the determinant. Since the determinant is not equal to 0, S –1 exists. A. Find the inverse of the matrix, if it exists.

10. Example 2 Find the Inverse of a Matrix Definition of inverse a = –1, b = 0, c = 8, d = –2 Simplify. Answer:

11. Example 2 Find the Inverse of a Matrix Check Find the product of the matrices. If the product is I, then they are inverse.

12. Example 2 Find the Inverse of a Matrix Find the value of the determinant. Answer: Since the determinant equals 0, T –1 does not exist. B. Find the inverse of the matrix, if it exists.

13. Example 2 A. Find the inverse of the matrix, if it exists. A.B. C.D.No inverse exists.

14. Example 2 B. Find the inverse of the matrix, if it exists. A.B. C.D.No inverse exists.

15. Example 3 Solve a System of Equations RENTAL COSTS The Booster Club for North High School plans a picnic. The rental company charges $15 to rent a popcorn machine and $18 to rent a water cooler. The club spends $261 for a total of 15 items. How many of each do they rent? A system of equations to represent the situation is as follows. x + y = 15 15x + 18y = 261

16. Example 3 Solve a System of Equations STEP 1 Find the inverse of the coefficient matrix. STEP 2 Multiply each side of the matrix equation by the inverse matrix.

17. Example 3 Solve a System of Equations Answer: The club rents 3 popcorn machines and 12 water coolers. The solution is (3, 12), where x represents the number of popcorn machines and y represents the number of water coolers.

18. Example 3 A.(–2, 4) B.(2, –4) C.(–4, 2) D.no solution Use a matrix equation to solve the system of equations. 3x + 4y = –10 x – 2y = 10

19. Homework Section 8 (pg 202): 13 – 37 odd, 38, 40, & 41(16 problems) 43 – 46 all(4 problems)

20. End of the Lesson