1. Today: Class Announcements Class Announcements Wednesday Warm-Up Wednesday Warm-Up 4.4 Notes 4.4 Notes Begin Homework Begin Homework Return 4.1-4.3 Quizzes Return 4.1-4.3 Quizzes

2. Try both problems on your own…

3. Vocabulary: identity matrix, inverse matrix identity matrix, inverse matrix Objectives: 1. Find the identity matrices 2. Find 2x2 inverse matrices 3. Find an inverse matrix using a calculator 4. Use inverse matrices to solve matrix equations

4. 5 + 0 = 5 because 0 is the additive identity 4 x 1 = 4 because 1 is the multiplicative identity Therefore, A x ? = A, ? will be the identity matrix. Dependent on the dimensions of A. If you need a 2x2 matrix  If you need a 3x3 matrix 

5. 5 + -5 = 0 because -5 is the additive inverse that gives the additive identity 2 x ½ = 1 because 1 is the multiplicative inverse that gives multiplicative identity Therefore, A x ? = I because ? is the inverse matrix that gives the identity matrix. What is the inverse matrix?

6. The inverse of matrix: Find the inverse of a square matrix: 1.Find the determinant of A 2.Switch the down and negate the up Determinant of A ≠ 0!

7. The inverse of matrix: Find the inverse of a square matrix: 1.Find the determinant of A 2.Switch the down and negate the up Determinant of A ≠ 0!

8. The inverse of matrix: Find the inverse of a square matrix: 1.Find the determinant of A 2.Switch the down and negate the up Determinant of A ≠ 0!

9. The inverse of matrix: Find the inverse of a matrix: 1.Input the matrix 2.On main screen, type matrix name with x -1 (inverse key) 3.Convert to fractions if desired

10. The inverse of matrix: Find the inverse of a matrix: 1.Input the matrix 2.On main screen, type matrix name with x -1 (inverse key) 3.Convert to fractions if desired

11. The inverse of matrix: Find the inverse of a matrix: 1.Input the matrix 2.On main screen, type matrix name with x -1 (inverse key) 3.Convert to fractions if desired

12. Why use inverse matrices? To solve equations! AX = B, solve for the mystery matrix X

13. Why use inverse matrices? To solve equations! AX = B, solve for the mystery matrix X

14. Why use inverse matrices? To solve equations! AX = B, solve for the mystery matrix X

15. Homework: pg. 227 #16, 18, 19, 25, 26, 29 pg. 227 #16, 18, 19, 25, 26, 29 CHAPTER 4 TEST ON THURSDAY, NOVEMBER 8 th ! CHAPTER 4 TEST ON THURSDAY, NOVEMBER 8 th !