Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

608 Chapter 18 Mathematics in Engineering

3 3 whose elements are computed by multiplying each element of matrix [A] by 5 as

shown here.

(18.11)

Multiplying a Matrix by Another Matrix Whereas any size matrix can be multiplied by a scalar quantity,

matrix multiplication can be performed only when the number of columns in thepremultiplier

matrix is equal to the number of rows in thepostmultipliermatrix. For example, matrix [A] of size

mncan be premultiplied by matrix [B] of sizenpbecause the number of columnsnin

matrix [A] is equal to number of rowsnin matrix [B]. Moreover, the multiplication results in

another matrix, say [C] of sizemp. Matrix multiplication is carried out according to the fol-

lowing rule. Consider the multiplication of the following 3 by 3 [A]andthe3by2[B] matrices.

Note the number of columns in matrix [A] is equal to number of rows in matrix [B], and the

multiplication will result in a matrix of size 3 by 2. The elements in the first column of the

resulting [C] matrix are computed from

and the elements in the second column of the [C] matrix are

If you are dealing with larger matrices, the elements in the other columns are computed

in a similar manner. Also, when multiplying matrices, keep in mind that matrix multiplication

is not commutative except for very special cases. That is,

3 A 43 B 4 3 B 43 A 4 (18.12)

£

78 1232122  192142  1112112

159 1232112  192162  1112152

150 12321  22  192132  1112182

§£

78 93

159 132

150 69

§

3 C 4 £

24 1

16 5

 23 8

§£

7

12 c

16 c

§£

78 c 12

159 c 22

150 c 32

§

(^23911) d
£
172122  1122142  1162112 c 12
172112  1122162  1162152 c 22
1721  22  1122132  1162182 c 32
§£
78 c 12
159 c 22
150 c 32
§
3 C 4 £
2 4 1
1 6 5
 2 3 8
§£
23
c 9
c 11
§
71216 d
3 A 43 B 4 £
241
165
 238
§
3  3
£
723
12 9
16 11
§
3  2
 3 C (^43)  2
53 A 4  5 £
40 1
29 2
5710
§£
20 0 5
10 45 10
25 35 50
§
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