2. Objectives  Add two matrices  Subtract two matrices  Multiply a matrix by a constant  Multiply two matrices

3. Matrix Addition The sum of two matrices with the same dimensions is the matrix that is formed by adding the corresponding entries of the two matrices. Addition is not defined if the matrices do not have the same number of rows and the same number of columns.

4. Example Find the following sums of matrices. a. b.

5. Example (cont) Find the following sums of matrices. c. A + B if A + B = The matrix that is the sum is called the ________matrix.

6. Matrix Subtraction If matrices M and N have the same dimension, the difference M  N is found by subtracting the elements of N from the corresponding elements of M. This difference can also be defined as M  N = M + (  N)

7. Example Complete the following matrix operations. a. b.

8. Product of a Number and a Matrix Multiplying a matrix A by a real number c results in a matrix in which each entry of matrix A is multiplied by the number c.

9. Example The table contains the purchase prices and delivery costs (per unit) for plywood, siding, and lumber. If the supplier announces a 5% increase in all of these prices and in delivery costs, find the matrix that gives the new prices and costs.

10. Example (cont) Use a matrix to represent the original prices and costs.

12. Example Compute the products AB and BA for the matrices

13. Example A business plans to use three methods of advertising— newspapers, radio, and cable TV—in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups: teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups. a. Does AB or BA give the matrix that represents the cost of ads for each target group in each market? b. Find this matrix. c. For what group of people is the most money spent on advertising?

14. Example (cont) a. Does AB or BA give the matrix that represents the cost of ads for each target group in each market? b. Find this matrix.

15. Example (cont)

16. c. For what group of people is the most money spent on advertising?

17. Example Use technology to compute BA and AB if

18. Example Use technology to compute BA and AB if

19. Assignment Pg. 531-535 #1-9 all #14-15 #17-20all #27-28 #34 and #39