1. 10/8/12 1)Notes 2)Worksheet for practice 3)HW: Page 175 # 13, 14, 17, 18, 21, 24, 26, 34 AND continue work on your project – DUE tomorrow!

2. Example 1 Analyze Data with Matrices A. Use the matrix below that includes information on tuition (T), room and board (R/B), and enrollment (E) for three universities. Find the average of the elements in column 1, and interpret the result. ISU UI UNI TR/BE

3. Example 1 Analyze Data with Matrices Answer: The average tuition cost for the three universities is $5935.

4. Example 1 Analyze Data with Matrices B. Use the matrix below that includes information on tuition (T), room and board (R/B), and enrollment (E) for three universities. Which university’s total cost is the lowest? ISU UI UNI TR/BE

5. Example 1 Analyze Data with Matrices ISU = 6160 + 5958 = $12,118 UI = 6293 + 7250 = $13,543 UNI = 5352 + 6280 = $11,632 Answer: University of Northern Iowa

6. Example 1 Analyze Data with Matrices C. Use the matrix below that includes information on tuition (T), room and board (R/B), and enrollment (E) for three universities. Would adding the elements of the rows provide meaningful data? Explain. ISU UI UNI TR/BE Answer: No, the first two elements of a row are in dollars and the third is in numbers of people.

7. Example 1 Analyze Data with Matrices D. Use the matrix below that includes information on tuition (T), room and board (R/B), and enrollment (E) for three universities. Would adding the elements of the third column provide meaningful data? Explain. ISU UI UNI TR/BE Answer: Yes, the sum of the elements of the third column would be the total enrollment of all three schools.

8. Concept

9. Example 2 Add and Subtract Matrices Substitution Add corresponding elements. Simplify. Answer:

10. Example 2 Add and Subtract Matrices Answer: Since the dimensions of A are 2 × 3 and the dimensions of B are 2 × 2, these matrices cannot be subtracted. –

11. Example 2 A. B. C. D.

12. Example 2 A. B. C. D.

13. Concept

14. Example 3 Multiply a Matrix by a Scalar Substitution

15. Example 3 Multiply a Matrix by a Scalar Multiply each element by 2. Answer: Simplify.

16. Example 3 A.B. C.D.

17. Concept

18. Example 4 Multi-Step Operations Perform the scalar multiplication first. Then subtract the matrices. Substitution Distribute the scalars in each matrix. 4A – 3B

19. Example 4 Multiply. Subtract corresponding elements. Answer: Simplify. Multi-Step Operations

20. Example 4 A. B. C. D.

21. Example 5 Use Multi-Step Operations with Matrices BUSINESS A small company makes unfinished desks and cabinets. Each item requires different amounts of hardware as shown in the matrices. DESK ShortLong Nails Screws CABINET ShortLong Nails Screws The company has orders for 3 desks and 4 cabinets. Express the company’s total needs for hardware in a single matrix.

22. Example 5 Use Multi-Step Operations with Matrices Write matrices. Multiply scalars. Add matrices. ShortLong Nails Screws Answer:

23. Example 5 Miniature golf course A has 50 blue golf balls, 100 yellow golf balls, and 50 green golf balls. Miniature golf course B has 150 blue golf balls, 100 yellow golf balls, and 25 green golf balls. Miniature golf course C has 40 blue golf balls, 70 yellow golf balls, and 80 green golf balls. Express the total number of each color golf ball in a single matrix. Blue Yellow Green A.B. C.D. Blue Yellow Green Course A Course B Course C Course A Course B Course C