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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. Solve each system of equations.4x – 2y + 5z = 362x + 5y – z = –8–3x + y + 6z = 13 A. (4, –5, 2) B. (3, –2, 4) C. (3, –1, 9) D. no solution 5-Minute Check 1

  4. Solve each system of equations.4x – 2y + 5z = 362x + 5y – z = –8–3x + y + 6z = 13 A. (4, –5, 2) B. (3, –2, 4) C. (3, –1, 9) D. no solution 5-Minute Check 1

  5. Solve each system of equations.x + 4y – 5z = 29–4x + 2y + z = –223x – 3y + 4z = –4 A. (0, 1, –5) B. (–2, 4, –3) C. (5, 1, –4) D. infinite solutions 5-Minute Check 2

  6. Solve each system of equations.x + 4y – 5z = 29–4x + 2y + z = –223x – 3y + 4z = –4 A. (0, 1, –5) B. (–2, 4, –3) C. (5, 1, –4) D. infinite solutions 5-Minute Check 2

  7. Solve each system of equations.2x + 6y – 3z = 12–5x – 2y + z = 66x – 8y + 4z = –35 A. (6, 1, 2) B. (–3, 3, 0) C. (3, –1, –4) D. no solution 5-Minute Check 3

  8. Solve each system of equations.2x + 6y – 3z = 12–5x – 2y + z = 66x – 8y + 4z = –35 A. (6, 1, 2) B. (–3, 3, 0) C. (3, –1, –4) D. no solution 5-Minute Check 3

  9. Solve each system of equations.3x + y – 4z = –7–2x – 5y + 8z = 85x + 2y + 3z = –22 A. (–3, –2, –1) B. (3, –4, 3) C. (–2, 3, 1) D. no solution 5-Minute Check 3

  10. Solve each system of equations.3x + y – 4z = –7–2x – 5y + 8z = 85x + 2y + 3z = –22 A. (–3, –2, –1) B. (3, –4, 3) C. (–2, 3, 1) D. no solution 5-Minute Check 3

  11. Mark sold three flavors of drinks at the local fair; cherry, grape, and orange. He sold twice as many cherry drinks as oranges drinks and he sold 6 more grape drinks than orange drinks. If he sold 54 total drinks, how many of each flavor did he sell? A.12 cherry, 18 grape, 24 orange B. 24 cherry, 12 grape, 18 orange C.24 cherry, 18 grape, 12 orange D.16 cherry, 14 grape, 8 orange 5-Minute Check 5

  12. Mark sold three flavors of drinks at the local fair; cherry, grape, and orange. He sold twice as many cherry drinks as oranges drinks and he sold 6 more grape drinks than orange drinks. If he sold 54 total drinks, how many of each flavor did he sell? A.12 cherry, 18 grape, 24 orange B. 24 cherry, 12 grape, 18 orange C.24 cherry, 18 grape, 12 orange D.16 cherry, 14 grape, 8 orange 5-Minute Check 5

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

  14. scalar • scalar multiplication Vocabulary

  15. 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

  16. Analyze Data with Matrices Answer: Example 1

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

  18. 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

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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. _ 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

  27. _ 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

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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

  33. 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

  34. Concept

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

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

  37. – Add and Subtract Matrices Answer: Example 2

  38. – 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

  39. A. B. C. D. Example 2

  40. A. B. C. D. Example 2

  41. A. B. C. D. Example 2

  42. A. B. C. D. Example 2

  43. Concept

  44. Multiply a Matrix by a Scalar Substitution Example 3

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

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

  47. A.B. C.D. Example 3

  48. A.B. C.D. Example 3

  49. Concept

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

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