See Problem 5.

Determine whether the product exists.

F = [ 2 3 6 9 ] G = [ − 3 6 2 − 4 ] H = [ − 5 6 ] J = [ 0 7 ] f equals . matrix with 2 rows and 2 columns , row1 column 1 , 2 , column 2 3 , row2 column 1 , 6 , column 2 9 , end matrix . g equals . matrix with 2 rows and 2 columns , row1 column 1 , negative 3 , column 2 6 , row2 column 1 , 2 , column 2 negative 4 , end matrix . h equals . matrix with 2 rows and 1 column , row1 column 1 , negative 5 , row2 column 1 , 6 , end matrix j equals left bracket 0 7 right bracket

29. FG
30. GF
31. FH
32. HG
33. JH

B Apply

34. Think About a Plan A hardware store chain sells hammers for $3, flashlights for $5, and lanterns for $7. The store manager tracks the daily purchases at three of the chain's stores in a 3 × 3 3 times 3  matrix. What is the total gross revenue from the flashlights sold at all three stores?

      Number of Items Sold   Store A Store B Store C   Hammers Flashlights Lanterns [ 10 9 8 3 14 6 2 5 7 ] table with 3 rows and 2 columns , row1 column 1 , , column 2 cap numberofcap itemscap sold , row2 column 1 , , column 2 table with 1 row and 3 columns , row1 column 1 , cap storecap a , column 2 cap storecap b , column 3 cap storecap c , end table , row3 column 1 , , column 2 table with 1 row and 2 columns , row1 column 1 , table with 3 rows and 1 column , row1 column 1 , cap hammers , row2 column 1 , cap flashlights , row3 column 1 , cap lanterns , end table , column 2 . matrix with 3 rows and 3 columns , row1 column 1 , 10 , column 2 9 , column 3 8 , row2 column 1 , 3 , column 2 14 , column 3 6 , row3 column 1 , 2 , column 2 5 , column 3 7 , end matrix , end table , end table

    • How can you use matrix multiplication to solve this problem?
    • What does the product matrix represent?
35. Sports Two teams are competing in a two-team track meet. Points for individual events are awarded as follows: 5 points for first place, 3 points for second place, and 1 point for third place. Points for team relays are awarded as follows: 5 points for first place and no points for second place.

    1. Use matrix operations to determine the score in the track meet.

       	Individual Events			Relays
       Team	First	Second	Third	First	Second
       West River	8	5	2	8	5
       River's Edge	6	9	12	6	9

    2. Who would win if the scoring was changed to 5 points for first place, 2 points for second place, and 1 point for third place in each individual event and 5 points for first place and 0 points for second place in a relay?

For Exercises 36–43, use matrices D, E, and F. Perform the indicated operations if they are defined. If an operation is not defined, label it undefined.

D = [ 1 2 − 1 0 3 1 2 − 1 − 2 ] E = [ 2 − 5 0 1 0 − 2 3 1 1 ] F = [ − 3 2 − 5 1 2 4 ] d equals . matrix with 3 rows and 3 columns , row1 column 1 , 1 , column 2 2 , column 3 negative 1 , row2 column 1 , 0 , column 2 3 , column 3 1 , row3 column 1 , 2 , column 2 negative 1 , column 3 negative 2 , end matrix . e equals . matrix with 3 rows and 3 columns , row1 column 1 , 2 , column 2 negative 5 , column 3 0 , row2 column 1 , 1 , column 2 0 , column 3 negative 2 , row3 column 1 , 3 , column 2 1 , column 3 1 , end matrix . f equals . matrix with 3 rows and 2 columns , row1 column 1 , negative 3 , column 2 2 , row2 column 1 , negative 5 , column 2 1 , row3 column 1 , 2 , column 2 4 , end matrix

36. DE
37. − 3 F negative 3 f
38. (DE)F
39. D(EF)
40. D − 2 E d minus , 2 e
41. ( E − D ) F open e minus d close f
42. (DD)E
43. (2D)(3F)
44. Writing Suppose A is a 2 × 3 2 times 3  matrix and B is a 3 × 2 3 times 2  matrix with elements not all being equal. Are AB and BA equal? Explain your reasoning. Include examples.

Table of Contents