B Apply

Find each matrix sum or difference if possible. If not possible, explain why.

A = [ 3 4 6 − 2 1 0 ] B = [ − 3 1 2 − 4 − 1 5 ] C = [ 1 2 − 3 1 ] D = [ 5 1 0 2 ] eh equals left bracket . table with 3 rows and 2 columns , row1 column 1 , 3 , column 2 4 , row2 column 1 , 6 , column 2 negative 2 , row3 column 1 , 1 , column 2 0 , end table . right bracket . b equals left bracket . table with 3 rows and 2 columns , row1 column 1 , negative 3 , column 2 1 , row2 column 1 , 2 , column 2 negative 4 , row3 column 1 , negative 1 , column 2 5 , end table . right bracket . c equals left bracket . table with 2 rows and 2 columns , row1 column 1 , 1 , column 2 2 , row2 column 1 , negative 3 , column 2 1 , end table . right bracket . d equals left bracket . table with 2 rows and 2 columns , row1 column 1 , 5 , column 2 1 , row2 column 1 , 0 , column 2 2 , end table . right bracket

19. A + B eh plus b
20. B + D b plus d
21. C + D c plus d
22. B − A b minus eh
23. C − D cap c minus d

24. Think About a Plan The table shows the number of beach balls produced during one shift at two manufacturing plants. Plant 1 has two shifts per day and Plant 2 has three shifts per day. Write matrices to represent one day's total output at the two plants. Then find the difference between daily production totals at the two plants.

    Beach Ball Production Per Shift

    	1-color		3-color
    	Plastic	Rubber	Plastic	Rubber
    Plant 1	500	700	1300	1900
    Plant 2	400	1200	600	1600

    • How can you use the number of shifts to find the total daily production totals at each plant?
    • What matrix equation can you use to solve this problem?

25. Sports The modern pentathlon is a grueling all-day competition. Each member of a team competes in five events: target shooting, fencing, swimming, horseback riding, and cross-country running. Here are scores for the U.S. women at the 2004 Olympic Games.

    U.S. Women's Pentathlon Scores, 2004 Olympics

    Event	Anita Allen	Mary Beth lagorashvili
    Shooting	952	760
    Fencing	720	832
    Swimming	1108	1252
    Riding	1172	1144
    Running	1044	1064

    SOURCE: Athens 2004 Olympic Games

    1. Write two 5 × 1 5 times 1  matrices to represent each woman's scores for each event.
    2. Find the total score for each athlete.

26. Data Analysis Refer to the table below.

    U.S. Participation (millions) in Selected Leisure Activities

    Activity	Male	Female
    Movies	59.2	65.4
    Exercise Programs	54.3	59.0
    Sports Events	40.5	31.1
    Home Improvement	45.4	41.8

    SOURCE: U.S. National Endowment for the Arts

    1. Add two matrices to find the total number of people participating in each activity.
    2. Subtract two matrices to find the difference between the numbers of males and females in each activity.
    3. Reasoning In part (b), does the order of the matrices matter? Explain.
27. Writing Given a matrix A, explain how to find a matrix B such that A + B = 0 . eh plus b equals 0 .

Solve each equation for each variable.

28. [ 4 b + 2 − 3 4 d − 4 a 2 3 2 f − 1 − 14 1 ] = [ 11 2 c − 1 0 − 8 2 3 0 3 g − 2 1 ] left bracket . table with 3 rows and 3 columns , row1 column 1 , 4 b plus 2 , column 2 negative 3 , column 3 4 d , row2 column 1 , negative 4 eh , column 2 2 , column 3 3 , row3 column 1 , 2 f minus 1 , column 2 negative 14 , column 3 1 , end table . right bracket equals left bracket . table with 3 rows and 3 columns , row1 column 1 , 11 , column 2 2 c minus 1 , column 3 0 , row2 column 1 , negative 8 , column 2 2 , column 3 3 , row3 column 1 , 0 , column 2 3 g minus 2 , column 3 1 , end table . right bracket
29. [ 4 c 2 − d 5 − 3 − 1 2 0 − 10 15 ] = [ 2 c + 5 4 d g − 3 h f − g 0 − 4 c 15 ] left bracket . table with 3 rows and 3 columns , row1 column 1 , 4 c , column 2 2 minus d , column 3 5 , row2 column 1 , negative 3 , column 2 negative 1 , column 3 2 , row3 column 1 , 0 , column 2 negative 10 , column 3 15 , end table . right bracket equals left bracket . table with 3 rows and 3 columns , row1 column 1 , 2 c plus 5 , column 2 4 d , column 3 g , row2 column 1 , negative 3 , column 2 h , column 3 f minus g , row3 column 1 , 0 , column 2 negative 4 c , column 3 15 , end table . right bracket

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