2. Operations and Applications

3.  Each number in a matrix is a matrix element.  A matrix element is identified by its position (row # and column #) within the matrix.

4. A = 175307175307 Element a 13 is the element in the 1 st row and the 3 rd column. Element a 13 is 5.

5. Identify each matrix element. K = 3 –1 –8 5 1 8 4 9 8 –4 7 –5 a. k 12 b. k 32 c. k 23 d. k 34 Element k 12 is –1.Element k 32 is –4. a. K = k 12 is the element in the first row and second column. 3 –1 –8 5 1 8 4 9 8 –4 7 –5 b. K = k 32 is the element in the third row and second column. 3 –1 –8 5 1 8 4 9 8 –4 7 –5

6. K = 3 –1 –8 5 1 8 4 9 8 –4 7 –5 a. k 12 b. k 32 c. k 23 d. k 34 Element k 23 is 4.Element k 34 is –5. c. K = k 23 is the element in the second row and third column. 3 –1 –8 5 1 8 4 9 8 –4 7 –5 d. K = k 34 is the element in the third row and the fourth column. 3 –1 –8 5 1 8 4 9 8 –4 7 –5

7. Three students kept track of the games they won and lost in a chess competition. They showed their results in a chart. Write a 2  3 matrix to show the data. Let each row represent the number of wins and losses and each column represent a student. = Win X = Loss Ed X X Jo X Lew X X X X 5 6 3 2 1 4 Wins Losses Ed Jo Lew

8. Algebra 2EnglishPhys EdFrench 2 Frank Fakename 93788798 Pamela Pretend 97899165 Jimmy Imaginary 86618895 Grades of several CHS students last marking period: Write a matrix G to represent this data.

9. 937887 98 978991 65 866188 95 G = Each column represents a different class. Each row represents a different student. What does element g 23 represent? Element g 23 is 91, and it represents Pamela Pretend’s grade in Phys Ed.

10. Refer to the table. a.Write a matrix N to represent the information. U.S. Passenger Car Imports And Exports (millions) 1980 1990 1995 Imports3.1163.9454.115 Exports0.6170.7940.989 Source: U.S. Department of Commerce. Use 2  3 matrix. 3.116 3.945 4.115 0.617 0.794 0.989 N = Import Exports 1980 1990 1995 Each column represents a different year. Each row represents imports and exports.

11. b.Which element represents exports for 1995? U.S. Passenger Car Imports And Exports (millions) 1980 1990 1995 Imports3.1163.9454.115 Exports0.6170.7940.989 Source: U.S. Department of Commerce. Exports are in the second row. The year 1995 is in the third column. Element n 23 represents the number of exports for 1995.

12. Another Example: At Domino's you can get any large pizza for $12 and an order of wings for $4.50. At Papa John's you can get a large pizza for $10 and an order of wings for $6. We can organize this into a matrix with the food as the rows and restaurants as the columns. We will call this matrix B. Pizza Wings Domino’sPapa John’s

15. You decide to order 4 large pizzas and 3 orders of wings. Calculate the total at each restaurant. Which restaurant should we go to? Pizza Wings Domino’sPapa John’s Domino’s = $65.64 Papa John’s = $61.95 Papa John’s

16. You Try: For breakfast Yoko had cereal, a banana, a cup of milk, and a slice of toast. She recorded the following information in her food journal. Cereal: 165 cal, 3g fat, 33 g carbs and no cholesterol. Banana: 120 cal, no fat, 26 g carbs, and no cholesterol. Milk: 120 cal, 5 g fat, 11 g carbs, and 15 mg cholesterol. Toast: 125 cal, 6 g fat, 14 g carbs, and 18 mg cholesterol. Write this information in a matrix N whose rows represent the foods. Label the rows and columns of your matrix. Cereal Banana Milk Toast Calories Fat Carbs Choles

17. Some Questions 1. State the values of N 23, N 32, and N 42. 2. Write an interpretation of N 23, N 32, and N 42. N 23 = 26 Banana Carbs N 32 = 5 Milk fat N 42 = 6 Toast fat

18. If Yoko has 1 bowl of cereal, 1 banana, 2 cups of milk, and two slices of toast, how many total calories will she have for breakfast. 775 Calories