4.1.2 Multiplying Matrices − Worksheet
Example 1: Tell whether each product is defined. If so, give its dimensions. 1. A 4 × 5 and B 5 × 3 ; AB 2. A 4 × 5 and B 5 × 3 ; BA
3. C 9
and D 5
; CD
× 5
× 9
4. C 9
5. E 6
6. E 6
and D 5
; DC
and F 2
; EF
and F 2
; FE
× 5
× 9
× 2
× 6
× 2
× 6
Example 2: Use the following matrices for Exercises 7-12. Find each product, if possible.
− 3 1 5 2 0 1
−
= B
= C
= I
1 0 0 1
0 7 3 2 3 0
− 4 2 1 3
− 3 1 7 10 1 1 3 5 −
A
D
=
=
−
7. BA
8. CA
9. CB
10. DC
11. BI
12. IB
Example 3: 13. Students collected recyclables for fund-raising over a three-week period. Use matrix multiplication to find the total amount of money collected for each type of item.
Recyclables Collected (lb)
Price Per Pound ($) Week Glass Cans Newspaper Office Paper 1 0.02 0.70 0.02 1.06 2 0.02 0.55 0.01 1.00 3 0.01 0.42 0.02 1.03
Item Week 1
Week 2
Week 3
Glass Cans
29 25 16
8 11
6
Newspaper Office paper
163 127 206 53 107 84
195
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