Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Find each sum or difference.

8. [ 1 − 1 0 1 ] + [ 0 1 1 − 1 ] . matrix with 2 rows and 2 columns , row1 column 1 , 1 , column 2 negative 1 , row2 column 1 , 0 , column 2 1 , end matrix . plus . matrix with 2 rows and 2 columns , row1 column 1 , 0 , column 2 1 , row2 column 1 , 1 , column 2 negative 1 , end matrix
9. [ − 3 6 2 0 ] − [ − 2 5 2 0 ] . matrix with 2 rows and 2 columns , row1 column 1 , negative 3 , column 2 6 , row2 column 1 , 2 , column 2 0 , end matrix . minus . matrix with 2 rows and 2 columns , row1 column 1 , negative 2 , column 2 5 , row2 column 1 , 2 , column 2 0 , end matrix
10. [ 5 2 − 1 8 ] − [ 7 − 4 0 2 ] . matrix with 2 rows and 2 columns , row1 column 1 , 5 , column 2 2 , row2 column 1 , negative 1 , column 2 8 , end matrix . minus . matrix with 2 rows and 2 columns , row1 column 1 , 7 , column 2 negative 4 , row2 column 1 , 0 , column 2 2 , end matrix
11. [ 4 − 1 2 0 3 5 ] + [ − 2 0 3 − 1 − 3 5 ] . matrix with 3 rows and 2 columns , row1 column 1 , 4 , column 2 negative 1 , row2 column 1 , 2 , column 2 0 , row3 column 1 , 3 , column 2 5 , end matrix . plus . matrix with 3 rows and 2 columns , row1 column 1 , negative 2 , column 2 0 , row2 column 1 , 3 , column 2 negative 1 , row3 column 1 , negative 3 , column 2 5 , end matrix
12. [ 0 0.4 − 2 5.3 1.2 3.7 ] + [ 1.8 − 5 7.1 0 0.3 2.3 ] . matrix with 3 rows and 2 columns , row1 column 1 , 0 , column 2 0.4 , row2 column 1 , negative 2 , column 2 5.3 , row3 column 1 , 1.2 , column 2 3.7 , end matrix . plus . matrix with 3 rows and 2 columns , row1 column 1 , 1.8 , column 2 negative 5 , row2 column 1 , 7.1 , column 2 0 , row3 column 1 , 0.3 , column 2 2.3 , end matrix
13. [ 4.7 − 0.3 2.9 0.7 − 3.5 1.3 ] − [ 2.3 7.3 − 5.1 0.4 4.2 0 ] . matrix with 3 rows and 2 columns , row1 column 1 , 4.7 , column 2 negative 0.3 , row2 column 1 , 2.9 , column 2 0.7 , row3 column 1 , negative 3.5 , column 2 1.3 , end matrix . minus . matrix with 3 rows and 2 columns , row1 column 1 , 2.3 , column 2 7.3 , row2 column 1 , negative 5.1 , column 2 0.4 , row3 column 1 , 4.2 , column 2 0 , end matrix

See Problem 2.

Find each product.

14. 4 [ 6 − 3 0 5 ] 4 . matrix with 2 rows and 2 columns , row1 column 1 , 6 , column 2 negative 3 , row2 column 1 , 0 , column 2 5 , end matrix
15. − 2 [ 3 − 1 7 − 2 ] negative 2 . matrix with 2 rows and 2 columns , row1 column 1 , 3 , column 2 negative 1 , row2 column 1 , 7 , column 2 negative 2 , end matrix
16. 0 [ 5.3 − 7.2 − 1.8 0.6 ] 0 . matrix with 2 rows and 2 columns , row1 column 1 , 5.3 , column 2 negative 7.2 , row2 column 1 , negative 1.8 , column 2 0.6 , end matrix
17. − 5 [ 3.8 2.1 7 9.4 − 6 0 ] negative 5 . matrix with 2 rows and 3 columns , row1 column 1 , 3.8 , column 2 2.1 , column 3 7 , row2 column 1 , 9.4 , column 2 negative 6 , column 3 0 , end matrix
18. 2.7 [ 3 4.7 0 − 3 5.7 2.7 ] 2.7 . matrix with 3 rows and 2 columns , row1 column 1 , 3 , column 2 4.7 , row2 column 1 , 0 , column 2 negative 3 , row3 column 1 , 5.7 , column 2 2.7 , end matrix
19. − 3.1 [ 4 7.5 9 − 5 1 4.6 ] negative 3.1 . matrix with 3 rows and 2 columns , row1 column 1 , 4 , column 2 7.5 , row2 column 1 , 9 , column 2 negative 5 , row3 column 1 , 1 , column 2 4.6 , end matrix
20. 8.3 [ − 1 8.2 0.3 − 4.1 6.2 9.5 ] 8.3 . matrix with 3 rows and 2 columns , row1 column 1 , negative 1 , column 2 8.2 , row2 column 1 , 0.3 , column 2 negative 4.1 , row3 column 1 , 6.2 , column 2 9.5 , end matrix
21. − 0.2 [ 8.3 − 3 0 4.5 5.6 1 − 1 2.9 7 ] negative 0.2 . matrix with 3 rows and 3 columns , row1 column 1 , 8.3 , column 2 negative 3 , column 3 0 , row2 column 1 , 4.5 , column 2 5.6 , column 3 1 , row3 column 1 , negative 1 , column 2 2.9 , column 3 7 , end matrix

    See Problem 3.

22. Sports For a certain city, the tables below show the numbers of participants in various sports in 2005 and 2010. Which sport had the greatest numerical increase in student participation between 2005 and 2010? Find your answer using matrices.

    Sports Participation, 2005

    Sport	Students	Adults
    Baseball	739	215
    Basketball	1023	437
    Football	690	58
    Soccer	1546	42

    Sports Participation, 2010

    Sport	Students	Adults
    Baseball	892	351
    Basketball	1114	483
    Football	653	64
    Soccer	1712	37

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