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Splash Screen. Five-Minute Check (over Lesson 3–4) Then/Now New Vocabulary Example 1: Real-World Example: Analyze Data with Matrices Key Concept: Adding and Subtracting Matrices Example 2: Add and Subtract Matrices Key Concept: Multiplying by a Scalar

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 3–4) Then/Now New Vocabulary Example 1: Real-World Example: Analyze Data with Matrices Key Concept: Adding and Subtracting Matrices Example 2: Add and Subtract Matrices Key Concept: Multiplying by a Scalar Example 3: Multiply a Matrix by a Scalar Key Concept: Properties of Matrix Operations Example 4: Multi-Step Operations Example 5: Real-World Example: Use Multi-Step Operations with Matrices Lesson Menu

  3. Graph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum an minimum values of the given function for this region. 1 ≤ x ≤ 4, y ≥ x, y ≥ 2x + 3; f(x, y) = 3x – 2y • maximum: f(4, 4) = 4minimum: f(4, 11) = –10 • B. maximum: f(4, 11) = 10minimum: f(1, 1) = 1 • C. maximum: f(4, 4) = 4minimum: f(1, 5) = –7 • D. maximum: f(4, 11) = 10minimum: f(4, 4) = 4 5-Minute Check 1

  4. A company profits $3 for every widget it manufactures and $2 for every plinket it manufactures. It must make at least one widget and one plinket each hour, but cannot make more than 7 total widgets and plinkets in any hour. What is the most profit the company can make in any hour? A. $21 B. $20 C. $18 D. $5 5-Minute Check 2

  5. You organized data into matrices. • Analyze data in matrices. • Perform algebraic operations with matrices. Then/Now

  6. scalar • scalar multiplication Vocabulary

  7. T R/B E ISU UI UNI 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. Example 1

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

  9. T R/B E ISU UI UNI 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? Example 1

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

  11. T R/B E ISU UI UNI 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. Answer:No, the first two elements of a row are in dollars and the third is in numbers of people. Example 1

  12. T R/B E ISU UI UNI 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. Answer:Yes, the sum of the elements of the third column would be the total enrollment of all three schools. Example 1

  13. Execution Degree Score of Difficulty Dive 1 Dive 2 Dive 3 Dive 4 Dive 5 Dive 6 The matrix displays Karen’s diving scores for her 6 dives at a competition. The total score is found by multiplying the degree of difficulty by the execution score. Example 1

  14. _ A. The average number of dives is 8.36. B. The average score for the 6 dives is 8.36. C. The average execution for the 6 dives is 8.36. D. The average degree of difficulty for the 6 dives is 8.36. _ _ _ A. Find the average of the elements in column 1, and interpret the results. Example 1

  15. B.The matrix displays Karen’s diving scores for her 6 dives at a competition. The total score is found by multiplying the degree of difficulty by the execution score. Which dive’s total is the highest? A. dive 1 B. dive 3 C. dive 4 D. dive 6 Example 1

  16. C.The matrix displays Karen’s diving scores for her 6 dives at a competition. The total score is found by multiplying the degree of difficulty by the execution score. Would adding the elements of the rows provide meaningful data? Explain. A. Yes, adding the elements gives the total score. B. No, the last element of the row is the product of the first and second elements in the row. Example 1

  17. D.The matrix displays Karen’s diving scores for her 6 dives at a competition. The total score is found by multiplying the degree of difficulty by the execution score. Would finding the average of the last column provide meaningful data? A. Yes, the average of the last column would be the average score for all 6 dives in the competition. B. No, each score has a different degree of difficulty, so you can’t find the average. Example 1

  18. Concept

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

  20. – 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. Example 2

  21. A. B. C. D. Example 2

  22. A. B. C. D. Example 2

  23. Concept

  24. Multiply a Matrix by a Scalar Substitution Example 3

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

  26. A.B. C.D. Example 3

  27. Concept

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

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

  30. A. B. C. D. Example 4

  31. CABINET DESK Short Long Short Long Nails Nails Screws Screws 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. The company has orders for 3 desks and 4 cabinets. Express the company’s total needs for hardware in a single matrix. Example 5

  32. Answer: Short Long Nails Screws Use Multi-Step Operations with Matrices Write matrices. Multiply scalars. Add matrices. Example 5

  33. A.B. C.D. Blue Yellow Green Blue Yellow Green Course A Course B Course C Course A Course B Course C 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. Example 5

  34. End of the Lesson

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