1. Section 6-2: Matrix Multiplication, Inverses and Determinants There are three basic matrix operations. 1.Matrix Addition 2.Scalar Multiplication 3.Matrix Multiplication

2. Section 6-2: Matrix Multiplication, Inverses and Determinants Matrix Addition

3. Section 6-2: Matrix Multiplication, Inverses and Determinants Scalar Multiplication

4. Section 6-2: Matrix Multiplication, Inverses and Determinants Matrix Multiplication ◦ Not quite as obvious ◦ No counterpart/equivalent operation in the real number system

5. Section 6-2: Matrix Multiplication, Inverses and Determinants

6. Example:

7. Section 6-2: Matrix Multiplication, Inverses and Determinants Example:

8. Section 6-2: Matrix Multiplication, Inverses and Determinants

9. Remember that a multiplicative identity for real numbers is 1 because for any real number, a, 1 · a = a. The multiplicative identity n x n square matrix (square means number of rows equals number of columns), is called an identity matrix.

10. Section 6-2: Matrix Multiplication, Inverses and Determinants

11. You can write a system of equations as a system of matrices.

12. Section 6-2: Matrix Multiplication, Inverses and Determinants Example:

13. Section 6-2: Matrix Multiplication, Inverses and Determinants The multiplicative inverse of a square matrix is called an inverse matrix.

14. Section 6-2: Matrix Multiplication, Inverses and Determinants Example:

15. Section 6-2: Matrix Multiplication, Inverses and Determinants If matrix A has an inverse, it is said to be invertible, or nonsingular. A singular matrix does not have an inverse.

16. Section 6-2: Matrix Multiplication, Inverses and Determinants Example:

17. Section 6-2: Matrix Multiplication, Inverses and Determinants

18. Finding the determinant can be helpful in determining whether a matrix has an inverse.

19. Section 6-2: Matrix Multiplication, Inverses and Determinants Finding the determinant can be helpful in determining whether a matrix has an inverse.

20. Section 6-2: Matrix Multiplication, Inverses and Determinants Example:

21. Section 6-2: Matrix Multiplication, Inverses and Determinants

22. Example:

23. Section 6-2: Matrix Multiplication, Inverses and Determinants Example:

24. Section 6-2: Matrix Multiplication, Inverses and Determinants Homework: ◦ Page 383-384 ◦ #3, 6, 21, 23, 27, 30, 35, 39 ◦ To turn in: #20, 38  Show all work -- only use your calculator to check your work.