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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.

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4.7 Inverse Matrices and Systems

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  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

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