1. Use Inverse Matrices to Solve Linear Systems Objectives 1.To find the inverse of a square matrix 2.To solve a matrix equation using inverses 3.To solve a linear system using inverse matrices

2. Warm-Up Imagine you lived in a world that never defined subtraction or division. What would you do to get the same results?

3. Objective 1 You will be able to find the inverse of a square matrix

4. Identity Matrix

5. Identity Property of Matrix Multiplication

6. Exercise 1

7. Inverse Matrix

8. Exercise 2

9. Inverse Matrix (2x2)

10. Exercise 3

11. Exercise 4

13. Matrix Equations

14. How to solve a matrix equation Since matrix multiplication is not commutative, you must remember to always multiply on the same side.

15. Exercise 5

16. Exercise 6

17. You will be able to solve a linear system using inverse matrices

18. Exercise 7 Use an inverse matrix to solve the linear system.

19. Step 3Step 2 Step 1 Solving Systems using Inverses

20. Protip: Multiplying by Inverse When multiplying by an inverse matrix to solve a matrix equation, first multiply by the “sub- inverse” and then divide each element by the determinant. “Sub- inverse” 1 divided by the determinant

21. Exercise 8 Solve each system using inverse matrices.

22. Inverse Matrix (3x3)

24. Exercise 9

25. Exercise 10

26. Exercise 11 Solve the system using inverse matrices.

27. Exercise 12 Solve the system using inverse matrices.

28. 3.8: Use Inverse Matrices to Solve Linear Systems Objectives 1.To find the inverse of a square matrix 2.To solve a matrix equation using inverses 3.To solve a linear system using inverse matrices