1. 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems1 Warm-Up #2 Find the determinants: 1. 2. Use Cramer’s Rule to determine the solution: 3. 6 –2 3 4

2. 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems2 DBA 10 th graders 1D 2H 3C 4G 5C 6J 7A 8G 9B 10H 11B 12G 13C 14G 15B 16G 17C 18G 19D 20G 21C 22F 23D 24G 25A

3. 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems3 DBA 11 th graders 1D 2H 3C 4H 5B 6J 7D 8G 9B 10H 11B 12G 13D 14H 15B 16H 17B 18G 19C 20F 21B 22H 23C 24F 25C

4. 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems4 Pg 274 6.(1/5, -4/5) 7.No solution 8.Omit 9.(5/2, -1/4) 18.No solution 19.(1.27, 1.11) 20.No solution 21.(-14/3, 7/9) 25.Omit 26.63.75 sq. miles 27.17 sq units

5. 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems5 Matrix Inverses and Solving Systems Section 4.5 - Honors viet.dang@humble.k12.tx.usviet.dang@humble.k12.tx.us ©2007

6. 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems6 Definition 1 is the multiplicative inverse for real numbers because multiplying by a real number will make it equal to 1 Example: 1/3 x = 1 x = 3

7. 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems7 Inverse Matrices Inverse of the matrix is… Multiply the with the inverse matrix

8. 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems8 Example 1 Find the inverse of:

9. 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems9 Example 1 Find the inverse of:

10. 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems10 Example 2 Find the inverse of:

11. Determine whether these two matrices are inverses: 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems11 Example 3 and = yes

12. Determine whether these two matrices are inverses: 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems12 Your Turn and no

13. 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems13 Solving Matrix Equation When solving for variables in a matrix: 1.Write a matrix equation with the coefficients in one bracket and variables on one side and constants on other side 2.Find the inverse 3.Multiply the inverse with the constant and add 4.Check

14. Write a matrix equation for the system and solve using inverse matrix 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems14 Example 4 Step 1: Write the equation in matrix form =

15. Write a matrix equation for the system and solve using inverse matrix 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems15 Example 4 Step 2: Find the inverse =

16. Write a matrix equation for the system and solve using inverse matrix 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems16 Example 4 Step 3: Multiply the inverse with the constants and add them (4, 3)

17. Write a matrix equation for the system and solve using inverse matrix 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems17 Example 4 Step 4: Check

18. Write a matrix equation for the system and solve using inverse matrix 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems18 Example 5 Step 1: Write the equation in matrix form

19. Write a matrix equation for the system and solve using inverse matrix 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems19 Example 5 Step 2: Find the inverse

20. Write a matrix equation for the system and solve using inverse matrix 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems20 Example 5 Step 3: Multiply the inverse with constants (5, –2)

21. Write a matrix equation for the system and solve using inverse matrix 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems21 Your Turn (3, 1)

22. April paid $24 for 2 admission tickets to see a concert and 7 soft drinks. Alexander paid $46 for 4 admission tickets and 13 soft drinks. Use an inverse matrix to determine the amount of money of each admission ticket and soft drink. 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems22 Example 6 x = tickets, y = drinks Identify the variables Setup the system Solve for x

23. April paid $24 for 2 admission tickets to see a concert and 7 soft drinks. Alexander paid $46 for 4 admission tickets and 13 soft drinks. Use an inverse matrix to determine the amount of money of each admission ticket and soft drink. 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems23 Example 6 Solve for x Each ticket was worth $5 and each soft drink was worth $2

24. Pg 282 15, 17-21 odd, 22-24 all, 27a-d 10/11/2014 5:29 AM4.5 - Matrix Inverse and Solving Systems24 Assignment