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Discover how to analyze and perform algebraic operations with matrices. Learn to add, subtract, multiply with scalars, and apply multi-step operations. Explore real-world examples and understand matrix properties.

markhsmith
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Lesson Menu

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  1. 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

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

  3. scalar • scalar multiplication Vocabulary

  4. 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

  5. Analyze Data with Matrices Answer: Example 1

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

  7. 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

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

  9. 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

  10. 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: 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: Example 1

  13. 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

  14. Concept

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

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

  17. – Add and Subtract Matrices Answer: Example 2

  18. – 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

  19. A. B. C. D. Example 2

  20. A. B. C. D. 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. Multiply a Matrix by a Scalar Multiply each element by 2. Simplify. Answer: Example 3

  27. A.B. C.D. Example 3

  28. A.B. C.D. Example 3

  29. Concept

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

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

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

  33. A. B. C. D. Example 4

  34. A. B. C. D. Example 4

  35. 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

  36. Use Multi-Step Operations with Matrices Write matrices. Multiply scalars. Add matrices. Answer: Example 5

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

  38. 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

  39. 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

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