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Splash Screen. Five-Minute Check (over Lesson 3–5) Then/Now Example 1: Dimensions of Matrix Products Key Concept: Multiplying Matrices Example 2: Multiply Square Matrices Example 3: Real-World Example: Multiply Matrices Example 4: Test of the Commutative Property

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 3–5) Then/Now Example 1: Dimensions of Matrix Products Key Concept: Multiplying Matrices Example 2: Multiply Square Matrices Example 3: Real-World Example: Multiply Matrices Example 4: Test of the Commutative Property Example 5: Test of the Distributive Property Key Concept: Properties of Matrix Multiplication Lesson Menu

  3. A. B. C. D. Use matrices B and D to find D – B. 5-Minute Check 1

  4. A. B. C. D. Use matrices B and D to find D – B. 5-Minute Check 1

  5. A. B. C. D. Use matrices B and D to find 4B. 5-Minute Check 2

  6. A. B. C. D. Use matrices B and D to find 4B. 5-Minute Check 2

  7. C. D. A. B. Use matrices B and D to find 2B + 3D. 5-Minute Check 3

  8. C. D. A. B. Use matrices B and D to find 2B + 3D. 5-Minute Check 3

  9. A. B. C.D. The table shows weekday ticket prices for an amusement park. Ticket prices are doubled on weekends. Find the weekend ticket prices and express them as a matrix. 5-Minute Check 4

  10. A. B. C.D. The table shows weekday ticket prices for an amusement park. Ticket prices are doubled on weekends. Find the weekend ticket prices and express them as a matrix. 5-Minute Check 4

  11. A. B. C. D. Which of the following sums cannot be simplified? 5-Minute Check 5

  12. A. B. C. D. Which of the following sums cannot be simplified? 5-Minute Check 5

  13. You multiplied matrices by a scalar. • Multiply matrices. • Use the properties of matrix multiplication. Then/Now

  14. Dimensions of Matrix Products A. Determine whether the product of A3×4 and B4×2 is defined. If so, state the dimensions of the product. A ● B = AB 3 × 4 4 × 2 3 × 2 Answer: Example 1

  15. Dimensions of Matrix Products A. Determine whether the product of A3×4 and B4×2 is defined. If so, state the dimensions of the product. A ● B = AB 3 × 4 4 × 2 3 × 2 Answer: The inner dimensions are equal so the matrix product is defined. The dimensions of the product are 3 × 2. Example 1

  16. Dimensions of Matrix Products B. Determine whether the product of A3×2 and B4×3 is defined. If so, state the dimensions of the product. A ● B 3 × 2 4 × 3 Answer: Example 1

  17. Dimensions of Matrix Products B. Determine whether the product of A3×2 and B4×3 is defined. If so, state the dimensions of the product. A ● B 3 × 2 4 × 3 Answer: The inner dimensions are not equal, so the matrix product is not defined. Example 1

  18. A. Determine whether the matrix product is defined. If so, what are the dimensions of the product?A3×2 and B2×3 A. 3 × 3 B. 2 × 2 C. 3 × 2 D. The matrix product is not defined. Example 1

  19. A. Determine whether the matrix product is defined. If so, what are the dimensions of the product?A3×2 and B2×3 A. 3 × 3 B. 2 × 2 C. 3 × 2 D. The matrix product is not defined. Example 1

  20. B. Determine whether the matrix product is defined. If so, what are the dimensions of the product?A2×3 and B2×3 A. 2 × 3 B. 3 × 2 C. 2 × 2 D. The matrix product is not defined. Example 1

  21. B. Determine whether the matrix product is defined. If so, what are the dimensions of the product?A2×3 and B2×3 A. 2 × 3 B. 3 × 2 C. 2 × 2 D. The matrix product is not defined. Example 1

  22. Concept

  23. Multiply Square Matrices Example 2

  24. Multiply Square Matrices Step 1 Multiply the numbers in the first row of R by the numbers in the first column of S, add the products, and put the result in the first row, first column of RS. Example 2

  25. Multiply Square Matrices Step 2Multiply the numbers in the first row of R by the numbers in the second column of S, add the products,and put the result in the first row, second column of RS. Example 2

  26. Multiply Square Matrices Step 3 Multiply the numbers in the second row of R by the numbers in the first column of S, add the products,and put the result in the second row, first column of RS. Example 2

  27. Multiply Square Matrices Step 4 Multiply the numbers in the second row of R by the numbers in the second column of S, add the products,and put the result in the second row, second column of RS. Example 2

  28. Multiply Square Matrices Step 5 Simplify the product matrix. Answer: Example 2

  29. Multiply Square Matrices Step 5 Simplify the product matrix. Answer: Example 2

  30. A. B. C. D. Example 2

  31. A. B. C. D. Example 2

  32. Multiply Matrices CHESS Three teams competed in the final round of the Chess Club’s championships. For each win, a team was awarded 3 points and for each draw a team received 1 point. Which team won the tournament? Understand The final scores can be found by multiplying the wins and draws by the points for each. Example 3

  33. Results Points Multiply Matrices Plan Write the results from the championship and the points in matrix form. Set up the matrices so that the number of rows in the points matrix equals the number of columns in the results matrix. Example 3

  34. Multiply Matrices Solve Multiply the matrices. Write an equation. Multiply columns by rows. Example 3

  35. Total Points Blue Red Green Multiply Matrices Simplify. The labels for the product matrix are shown below. Example 3

  36. Multiply Matrices Answer: Example 3

  37. Multiply Matrices Answer: The red team won the championship with a total of 21 points. CheckR is a 3 × 2 matrix and P is a 2× 1 matrix. Their product should be a 3× 1 matrix. Example 3

  38. BASKETBALLIn Thursday night’s basketball game, three of the players made the points listed below in the chart. They scored 1 point for the free-throws, 2 points for the 2-point shots, and 3 points for the 3-points shots. Who scored the most points? A. Warton B. Bryant C. Chris D. none of the above Example 3

  39. BASKETBALLIn Thursday night’s basketball game, three of the players made the points listed below in the chart. They scored 1 point for the free-throws, 2 points for the 2-point shots, and 3 points for the 3-points shots. Who scored the most points? A. Warton B. Bryant C. Chris D. none of the above Example 3

  40. A. Find KL if K Test of the Commutative Property Substitution Multiply columns by rows. Simplify. Example 4

  41. Test of the Commutative Property Answer: Example 4

  42. Answer: Test of the Commutative Property Example 4

  43. B. Find LK if K Test of the Commutative Property Substitution Multiply columns by rows. Example 4

  44. Test of the Commutative Property Simplify. Answer: Example 4

  45. Test of the Commutative Property Simplify. Answer: Example 4

  46. A. B. C. D. Example 4

  47. A. B. C. D. Example 4

  48. A. B. C. D. Example 4

  49. A. B. C. D. Example 4

  50. A. Test of the Distributive Property Substitution Add corresponding elements. Example 5

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