1. 4.5, 4.6 2 x 2 and 3 x 3 Matrices, Determinants, and Inverses Date: _____________

2. Matrices are multiplicative inverses Page 199 – 2 definitions Multiplicative Identity Matrix – Must be a square matrix, 2 x 2, 3 x 3, 4 x 4, etc. – Has 1’s in the main diagonal and 0’s elsewhere Multiplicative Inverse of a Matrix – when multiplying a matrix by its inverse, we get the identity matrix

3. Use your calculator Matrices are multiplicative inverses Show that these two matrices are multiplicative inverses

4. Objective - To evaluate the determinates of 2 x 2 and 3 x 3 matrices. Determinant can be labeled either way Find the Determinant

5. Determinant Objective - To evaluate the determinates of 2 x 2 and 3 x 3 matrices. Find the Determinant

6. Evaluate the Determinant for each Matrix When the determinant = 0, then that matrix has NO INVERSE

7. Determinant Take the first 2 columns and rewrite them outside Find the determinant of each 3x3 Matrix.

13. Fun? Use your Calculator Matrix, over to MATH, then det(, then go to Matrix, we want matrix A

14. Determinant and its use The determinant is used to find our inverse We will use our calculator to find the inverse. Type in: Find the determinant first: Therefore, it has an inverse

15. Determinant and its use The determinant is used to find our inverse We will use our calculator to find the inverse. Type in:

16. Find the inverse of the matrix If A didn’t have an inverse, you’d get the message ERR: SINGULAR MAT

17. Checking your answers. If you multiply inverses, you will always get the identity matrix. This is a way you can check your answers

18. Solve for X. Linear EquationsMatrix Equations

19. Objective - To solve systems using inverse matrices.

20. Do this one on your own to see if you understand