1. Adding and Subtracting Matrices

2. What is the size/dimension?

3. Organize the following information about your CD collection Writing a Matrix Rap: 4 groups, 6 solo artists, 0 collections Rock: 8 groups, 3 solo artists, and 3 collections R & B: 1 group, 5 solo artists, 2 collections 46 0 83 3 15 2 4 81 6 35 0 32

4. Only matrices with the same dimensions can be added and subtracted. The resulting matrix has the same dimension of the two matrices being added or subtracted. Remember

5. Tell whether the matrices can be added 334456334456 334 9 456 8 + [[]] 23342334 6 7 3 418 4 3 [[ [[ ]] ] ] + +

6. To add two matrices, they must have the same order. To add, you simply add corresponding entries.

7. Example Add the corresponding elements in each matrix Be careful, there is a mistake here

8. Subtracting Matrices To subtract two matrices, they must have the same order. You simply subtract corresponding entries.

9. Try this

10. We cant add because they are different dimensions!!!

12. Questions? Other resources: http://www.intmath.com/matrices-determinants/matrix-multiplication- flash.php

13. Assessment

14. Organizing Data As we know, matrices are a useful way to organize and keep track of data. For example if you have a business, it is important to keep track of revenue (income) and expenses (costs). You can find how much profit has been made by subtracting expenses from revenue. Profit = Revenue – Expenses If the profit is negative, did you make any money?

15. Finding a Profit Matrix You own two stores that sell household appliances. The matrices on the board show revenue and expenses for three months at each store. You can find out how much profit has been made by subtracting expenses from revenue. If the profit is a negative number, you lost money!! Write a matrix that shows the monthly profit for each store. Which store had higher overall profits during the three- month period? What store lost money? In which month?

16. Closure Question Two matrices are added. Their sum is a matrix with all zero entries. What would need to be true about the matrices? What would need to be true about the corresponding entries of the matrices? Explain why matrices that are different sizes can not be added or subtracted?