1 / 36

4.7 Inverse Matrices and Systems

4.7 Inverse Matrices and Systems. 1) Inverse Matrices and Systems of Equations. You have solved systems of equations using graphing, substitution , elimination …oh my… In the “real world”, these methods take too long and are almost never used. Inverse matrices are more practical.

tyne
Download Presentation

4.7 Inverse Matrices and Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 4.7 Inverse Matrices and Systems

  2. 1) Inverse Matrices and Systems of Equations • You have solved systems of equations using graphing,substitution, elimination…oh my… • In the “real world”, these methods take too long and are almost never used. • Inverse matrices are more practical.

  3. 1) Inverse Matrices and Systems of Equations • For a • System of Equations

  4. 1) Inverse Matrices and Systems of Equations • For a We can write a • System of Equations Matrix Equation

  5. 1) Inverse Matrices and Systems of Equations • Example 1: • Write the system as a matrix equation

  6. 1) Inverse Matrices and Systems of Equations • Example 1: • Write the system as a matrix equation • Matrix Equation

  7. 1) Inverse Matrices and Systems of Equations • Example 1: • Write the system as a matrix equation • Matrix Equation Coefficient matrix Variable matrix Constant matrix

  8. 1) Inverse Matrices and Systems of Equations • Example 2:

  9. 1) Inverse Matrices and Systems of Equations • Example 2:

  10. 1) Inverse Matrices and Systems of Equations • Example 2: A X B

  11. 1) Inverse Matrices and Systems of Equations

  12. 1) Inverse Matrices and Systems of Equations When rearranging, take the inverse of A

  13. 1) Inverse Matrices and Systems of Equations The Plan… “Solve the system” using matrices and inverses

  14. 1) Inverse Matrices and Systems of Equations • Example 3: • Solve the system

  15. 1) Inverse Matrices and Systems of Equations • Example 3: • Solve the system • Step 1: Write a matrix equation

  16. 1) Inverse Matrices and Systems of Equations • Example 3: • Solve the system • Step 1: Write a matrix equation

  17. 1) Inverse Matrices and Systems of Equations • Example 3: • Solve the system • Step 2: Find the determinant and A-1

  18. 1) Inverse Matrices and Systems of Equations • Example 3: • Solve the system • Step 2: Find the determinant and A-1 Change signs Change places

  19. 1) Inverse Matrices and Systems of Equations • Example 3: • Solve the system • Step 2: Find the determinant and A-1 Change signs Change places detA = 4 – 3 = 1

  20. 1) Inverse Matrices and Systems of Equations • Example 3: • Solve the system • Step 2: Find the determinant and A-1

  21. 1) Inverse Matrices and Systems of Equations • Example 3: • Solve the system • Step 3: Solve for the variable matrix

  22. 1) Inverse Matrices and Systems of Equations • Example 3: • Solve the system • Step 3: Solve for the variable matrix

  23. 1) Inverse Matrices and Systems of Equations • Example 3: • Solve the system • Step 3: Solve for the variable matrix

  24. 1) Inverse Matrices and Systems of Equations • Example 3: • Solve the system • Step 3: Solve for the variable matrix The solution to the system is (4, 1).

  25. 1) Inverse Matrices and Systems of Equations • Example 4: • Solve the system. Check your answer.

  26. 1) Inverse Matrices and Systems of Equations • Example 4: • Solve the system. Check your answer.

  27. 1) Inverse Matrices and Systems of Equations • Example 4: • Solve the system. Check your answer. detA = 10 - 9 = 1

  28. 1) Inverse Matrices and Systems of Equations • Example 4: • Solve the system. Check your answer.

  29. 1) Inverse Matrices and Systems of Equations • Example 4: • Solve the system. Check your answer. The solution to the system is (-1, 4).

  30. 1) Inverse Matrices and Systems of Equations • Example 4: • Solve the system. Check your answer. • Check

  31. 1) Inverse Matrices and Systems of Equations • What about a matrix that has no inverse? • It will have no unique solution.

  32. 1) Inverse Matrices and Systems of Equations • Example 5: • Determine whether the system has a unique solution.

  33. 1) Inverse Matrices and Systems of Equations • Example 5: • Determine whether the system has a unique solution. • Find the determinant.

  34. 1) Inverse Matrices and Systems of Equations • Example 5: • Determine whether the system has a unique solution. • Find the determinant.

  35. 1) Inverse Matrices and Systems of Equations • Example 5: • Determine whether the system has a unique solution. • Find the determinant. Since detA = 0, there is no inverse. The system does not have a unique solution.

  36. Homework • p.217 #1-5, 7-10, 20, 21, 23, 24, 26, 27, 36 • DUE TOMORROW: Two codes • TEST: Wednesday Nov 25 • Chapter 4

More Related