1. Assignment Questions?? Pg. 184-185 15-17 all, 23-26, 35, 46, 48 Handout Questions?

2. Quiz Questions

3. Unit 1-8: Systems with Matrices

4. Concept

5. Example 1 Second-Order Determinant Definition of determinant Multiply. = 4Simplify. Answer: 4 Evaluate

6. Example 1 A.–2 B.2 C.6 D.1

7. A.–66 B.–48 C.20 D.160

8. Why is a determinant important? It determines if the matrix has an inverse or not. If the determinant equals 0, then the matrix has no inverse.

10. Concept

11. 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

12. 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.

13. Concept

14. 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.

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

16. 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.

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

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