4-1 Matrices and Data

Transcription

1 4-1 Matrices and Data Warm Up Lesson Presentation Lesson Quiz 2

2 The table shows the top scores for girls in barrel racing at the 2004 National High School Rodeo finals. The data can be presented in a table or a spreadsheet as rows and columns of numbers.

3 You can also use a matrix to show table data. A matrix is a rectangular array of numbers enclosed in brackets.

4 Objectives Use matrices to display mathematical and real-world data. Find sums, differences, scalar products and products of matrices.

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7 Does the dimension matter?

8 matrix dimensions entry address scalar Vocabulary

9 matrix dimensions entry address scalar Vocabulary

10 Matrix A has two rows and three columns. A matrix with m rows and n columns has dimensions m n, read m by n, and is called an m n matrix. A has dimensions 2 3. Each value in a matrix is called an entry of the matrix.

11 The address of an entry is its location in a matrix, expressed by using the lower case matrix letter with row and column number as subscripts. The score is located in row 2 column 1, so a 21 is

12 Example 1: Displaying Data in Matrix Form The prices for different sandwiches are presented at right. 6 in 9 in Roast beef $3.95 $5.95 Turkey $3.75 $5.60 Tuna $3.50 $5.25 A. Display the data in matrix form. P = B. What are the dimensions of P? P has three rows and two columns, so it is a 3 2 matrix.

13 Example 1: Displaying Data in Matrix Form The prices for different sandwiches are presented at right. 6 in 9 in Roast beef $3.95 $5.95 Turkey $3.75 $5.60 Tuna $3.50 $5.25 C. What is entry P 32? What does is represent? The entry at P 32, in row 3 column 2, is It is the price of a 9 in. tuna sandwich. D. What is the address of the entry 5.95? The entry 5.95 is at P 12.

14 Use matrix M to answer the questions below. Check It Out! Example 1 a. What are the dimensions of M? 3 4 b. What is the entry at m 32? 11 c. The entry 0 appears at what two addresses? m 14 and m 23

15 You can add or subtract two matrices only if they have the same dimensions.

16 Example 2A: Finding Matrix Sums and Differences Add or subtract, if possible. 3 2 W =, X =, Y =, 2 3 Z = W + Y

17 Example 2B: Finding Matrix Sums and Differences Add or subtract, if possible. 3 2 W =, X =, Y =, 2 3 Z = X Z

18 Example 2C: Finding Matrix Sums and Differences Add or subtract, if possible. 3 2 W =, X =, Y =, 2 3 Z = X + Y

19 Check It Out! Example 2A Add or subtract if possible. 4 2 A = 3 10, B =, C = 0 9, 5 14 D = B + D ( 3)

20 Check It Out! Example 2B Add or subtract if possible. 4 2 A = 3 10, B =, C = 0 9, 5 14 D = B A

21 Check It Out! Example 2C Add or subtract if possible. 4 2 A = 3 10, B =, C = 0 9, 5 14 D = D B

22 Write a short summary to explain how to add matrices.

23 Write a short summary to explain how to subtract matrices.

24 Scalar Multiplication 4 2 3A = A = ½ A =

25 Write a short summary to explain how to Multiply a matrix by a scalar (constant) value.

26 Evaluating equal matrices 2x-5 4 = y+12 3 y+18

27 x+8-5 = y 3 4y-10

28 x =

29 Example 4B: Simplifying Matrix Expressions P = Q= R = Evaluate 3R P, if possible. 3(1) 123(4) 3( 2) 6 9 3(3) 3(0) 0 123(4)

30 Example 4A: Simplifying Matrix Expressions P = Q= R = Evaluate 3P Q, if possible.

31 Write a short summary to explain how to solve matrix equations.

32 The product of an m n and an n p matrix is an m p matrix.

33 Let s work through this together

34 Let s work through this together

35 How do you finish the multiplication?

36 How do you finish the multiplication?

37 Find the products: 1. A 2

38 Find the products: 1. CB

39 Find the products: 1. BA

40 Find the products: 1. CD

41 Find the products: 1. BA

42 The product of two or more matrices is the matrix product. The following rules apply when multiplying matrices. The product of an m n and an n p matrix is an m p matrix.

43 The product of an m n and an n p matrix is an m p matrix.

44 Example 1A: Identifying Matrix Products Tell whether the product is defined. If so, give its dimensions. A 3 4 and B 4 2 ; AB A B AB = 3 2 matrix

45 Example 1B: Identifying Matrix Products Tell whether the product is defined. If so, give its dimensions. C 1 4 and D 3 4 ; CD C D The inner dimensions are not equal (4 3), so the matrix product is not defined.

46 Tell whether the product is defined. If so, give its dimensions. P 2 5 Q 5 3 R 4 3 S 4 5 QP Check It Out! Example 1a

47 Tell whether the product is defined. If so, give its dimensions. P 2 5 Q 5 3 R 4 3 S 4 5 SR Check It Out! Example 1b

48 Tell whether the product is defined. If so, give its dimensions. P 2 5 Q 5 3 R 4 3 S 4 5 SQ Check It Out! Example 1c

49 Write a short summary to explain how to find matrix products.

50 1. What are the dimensions of A? 2. What is entry D 12? Evaluate if possible. 3. A C 4. C + D 5. B + D