18.5 Matrix Algebra 609
This may be a good place to point out that if [I] is an identity matrix and [A] is a square matrix
of matching size, then it can be readily shown that the product of(18.13)
Example 18.1 Given matrices: perform
the following operations.
(a) [A] [B] ?
(b) [A] [B] ?
(c) 3[A] ?
(d) [A][B] ?
(e) [A]{C} ?
(f ) Show that [I][A] [A][I] [A]We will use the operation rules discussed in the preceding sections to answer these
questions.(a) [A] [B] ?
(b) [A] [B] ?
(c) 3[A] ?
33 A 4 3 £
050
837
9 29
§£
0 132152 0
132182132132132172
1321921321 22132192
§£
01 5 0
24 9 21
27 627
§
£
10 4215 6210 1 222
18 7213 22 17 32
19 121 2 3219 1 422
§£
4 12
114
8 513
§
3 A 4 3 B 4 £
050
837
9 29
§£
46 2
72 3
13 4
§
£
10 4215 6210 1 222
18 7213 2217 32
19 121 2 3219 1 422
SC
4 11 2
15 5 10
10 1 5
§
3 A 4 3 B 4 £
050
837
9 29
SC
46 2
72 3
13 4
§
3 A 4 £
050
837
9 29
§, 3 B 4 £
46 2
72 3
13 4
§, and 5 C 6 •
1
2
5
¶,
3 I 43 A 4 3 A 43 I 4 3 A 4
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