1. Warm Up

2. Inverse Matrices

3. Three main topics today Identity Matrix Determinant Inverse Matrix

4. Identity Matrices  An identity matrix is a square matrix that has 1’s along the main diagonal and 0’s everywhere else.  When you multiply a matrix by the identity matrix, you get the original matrix.

5. Determinant The determinant of a square matrix is a constant value that doesn’t have much meaning on its own, but finding it allows us to do other things with matrices. We will find determinants of 2x2 matrices by hand, and anything bigger on the calculator.

6. Determinants

7. Examples!

8. Find the determinant:

9. As stated before, this value of -30 doesn’t really do anything for us on its own, but we will see how we can use this value later.

10. Finding a 3x3 determinant is a pain to do by hand, we wil use the calculator for these. Enter this matrix into your calculator for matrix [A] Go back to homescreen Select Matrix ---Math---det( Select matrix ----Names----[A]---- Enter.

11. Inverse Matrix (A -1 ) The product of any square matrix A and its inverse matrix A -1 is equal to the identity matrix I. We can write this as A A -1 = A -1 A = I

12. For the square matrix A = Find the determinant, the inverse matrix A -1, and show that A A -1 = I. Example

13. Solution detA = det = (2  5) - (3  4) = 10 - 12 = -2 A -1 = =

14. AA -1 = Solution Continued

17. Homework: Inverses worksheet, all problems. http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Docum ents/4-5/4_5HW.pdf