Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Use matrices A, B, C, and D. Find each product, sum, or difference.

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 . matrix 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 matrix . b equals . matrix 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 matrix . c equals . matrix with 2 rows and 2 columns , row1 column 1 , 1 , column 2 2 , row2 column 1 , negative 3 , column 2 1 , end matrix . d equals . matrix with 2 rows and 2 columns , row1 column 1 , 5 , column 2 1 , row2 column 1 , 0 , column 2 2 , end matrix

7. 3A
8. 4B
9. − 3 C negative 3 c
10. − D negative d
11. A − 2 B eh minus , 2 b
12. 3 A + 2 B 3 eh plus 2 b
13. 4 C + 3 D 4 c plus 3 d
14. 2 A − 5 B 2 eh minus 5 b

See Problem 2.

Solve each matrix equation. Check your answers.

15. 3 [ 2 0 − 1 5 ] − 2 X = [ − 10 5 0 17 ] 3 . matrix with 2 rows and 2 columns , row1 column 1 , 2 , column 2 0 , row2 column 1 , negative 1 , column 2 5 , end matrix . minus 2 x equals . matrix with 2 rows and 2 columns , row1 column 1 , negative 10 , column 2 5 , row2 column 1 , 0 , column 2 17 , end matrix
16. 4 X + [ 1 3 − 7 9 ] = [ − 3 11 5 − 7 ] 4 x plus . matrix with 2 rows and 2 columns , row1 column 1 , 1 , column 2 3 , row2 column 1 , negative 7 , column 2 9 , end matrix . equals . matrix with 2 rows and 2 columns , row1 column 1 , negative 3 , column 2 11 , row2 column 1 , 5 , column 2 negative 7 , end matrix
17. 1 2 X + [ 4 − 3 12 1 ] = [ 2 1 1 2 ] 1 half x plus . matrix with 2 rows and 2 columns , row1 column 1 , 4 , column 2 negative 3 , row2 column 1 , 12 , column 2 1 , end matrix . equals . matrix with 2 rows and 2 columns , row1 column 1 , 2 , column 2 1 , row2 column 1 , 1 , column 2 2 , end matrix
18. 5 X − [ 1.5 − 3.6 − 0.3 2.8 ] = [ 0.2 1.3 − 5.6 1.7 ] 5 x minus . matrix with 2 rows and 2 columns , row1 column 1 , 1.5 , column 2 negative 3.6 , row2 column 1 , negative 0.3 , column 2 2.8 , end matrix . equals . matrix with 2 rows and 2 columns , row1 column 1 , 0.2 , column 2 1.3 , row2 column 1 , negative 5.6 , column 2 1.7 , end matrix

See Problem 3.

Find each product.

19. [ − 3 4 5 2 ] [ 1 0 2 − 3 ] . matrix with 2 rows and 2 columns , row1 column 1 , negative 3 , column 2 4 , row2 column 1 , 5 , column 2 2 , end matrix . matrix with 2 rows and 2 columns , row1 column 1 , 1 , column 2 0 , row2 column 1 , 2 , column 2 negative 3 , end matrix
20. [ 1 0 2 − 3 ] [ − 3 4 5 2 ] . matrix with 2 rows and 2 columns , row1 column 1 , 1 , column 2 0 , row2 column 1 , 2 , column 2 negative 3 , end matrix . matrix with 2 rows and 2 columns , row1 column 1 , negative 3 , column 2 4 , row2 column 1 , 5 , column 2 2 , end matrix
21. [ 0 2 − 4 0 ] [ 0 2 − 4 0 ] . matrix with 2 rows and 2 columns , row1 column 1 , 0 , column 2 2 , row2 column 1 , negative 4 , column 2 0 , end matrix . matrix with 2 rows and 2 columns , row1 column 1 , 0 , column 2 2 , row2 column 1 , negative 4 , column 2 0 , end matrix
22. [ − 3 5 ] [ − 3 5 ] . matrix with 1 row and 2 columns , row1 column 1 , negative 3 , column 2 5 , end matrix . matrix with 2 rows and 1 column , row1 column 1 , negative 3 , row2 column 1 , 5 , end matrix
23. [ − 3 5 ] [ − 3 0 5 0 ] . matrix with 1 row and 2 columns , row1 column 1 , negative 3 , column 2 5 , end matrix . matrix with 2 rows and 2 columns , row1 column 1 , negative 3 , column 2 0 , row2 column 1 , 5 , column 2 0 , end matrix
24. [ − 3 5 ] [ 0 − 3 0 5 ] . matrix with 1 row and 2 columns , row1 column 1 , negative 3 , column 2 5 , end matrix . matrix with 2 rows and 2 columns , row1 column 1 , 0 , column 2 negative 3 , row2 column 1 , 0 , column 2 5 , end matrix
25. [ 0 − 3 0 5 ] [ − 3 0 5 0 ] . matrix with 2 rows and 2 columns , row1 column 1 , 0 , column 2 negative 3 , row2 column 1 , 0 , column 2 5 , end matrix . matrix with 2 rows and 2 columns , row1 column 1 , negative 3 , column 2 0 , row2 column 1 , 5 , column 2 0 , end matrix
26. [ 1 0 − 1 − 5 0 3 ] [ − 1 0 0 − 1 ] . matrix with 3 rows and 2 columns , row1 column 1 , 1 , column 2 0 , row2 column 1 , negative 1 , column 2 negative 5 , row3 column 1 , 0 , column 2 3 , end matrix . matrix with 2 rows and 2 columns , row1 column 1 , negative 1 , column 2 0 , row2 column 1 , 0 , column 2 negative 1 , end matrix
27. [ − 1 3 − 3 2 − 2 1 ] [ 5 4 3 ] . matrix with 2 rows and 3 columns , row1 column 1 , negative 1 , column 2 3 , column 3 negative 3 , row2 column 1 , 2 , column 2 negative 2 , column 3 1 , end matrix . matrix with 3 rows and 1 column , row1 column 1 , 5 , row2 column 1 , 4 , row3 column 1 , 3 , end matrix

See Problem 4.

28. Business A florist makes three special floral arrangements. One uses three lilies. The second uses three lilies and four carnations. The third uses four daisies and three carnations. Lilies cost $2.15 each, carnations cost $.90 each, and daisies cost $1.30 each.
    1. Write a matrix to show the number of each type of flower in each arrangement.
    2. Write a matrix to show the cost of each type of flower.
    3. Find the matrix showing the cost of each floral arrangement.

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