January 2014
Intermediate to advanced
144 pages
4h 2m
English
Content preview from Mathematical Formulas for Industrial and Mechanical Engineering
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Example 2
Given matrix is A 5
1223
240 5
. Verify that ðA
T
Þ
T
5 A.
Solution
Here
A 5
1223
240 5
.A
T
5
1 24
20
235
0
@
1
A
.ðA
T
Þ
T
5
122 3
240 5
‘ ðA
T
Þ
T
5 A. Hence, it is verified.
Example
Suppose that a company puts a problem to you:
Determine which of the three methods M
1
, M
2
, and M
3
of production it should use in
producing three goods A, B, and C. The amount of each good produced by each method is
shown below in matrix form:
ABC
M
1
M
2
M
3
463
595
347
0
@
1
A
The row matrix ð30 45 42 Þ represents the profit per unit for the goods A, B, and C,
respectively. Use matrix multiplication to decide which method maximizes the total profit.
Solution
Let P 5
463
595
347
0
@
1
A
and Q 5 ð30 45 42 Þ.
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