Page 65 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes (i) The total requirement of each material is given by
P 1 P 2 P 3
M 1 2 4 2 100 P 1 800
A¢B = M 2 3 2 4 100 P 2 900
M 1 5 2 100 P 800
3 3
(ii) The per unit cost production of each product is given by
M 1 M 2 M 3
P 1 2 3 1 5 45
AC = P 2 4 2 5 10 65
P 2 4 2 5 60
3
(iii) The total cost of production of 200 units of each product

45
200 200 200 65 = 9000 + 13000 + 12000 = 34000.
60

Tasks
A manufacturer produces three products A, B and C, which are sold in Delhi and Calcutta.
The annual sales of these products are given below:
Product
A B C
Delhi 5000 7500 15000
Calcutta 9000 12000 8700
If the sale price of the products A, B and C per unit be 2, 3 and 4 respectively,
calculate total revenue from each centre by using matrices.

3.5 Transpose of a Matrix

If A is a matrix of order m , n then the matrix obtained by interchanging the rows and columns
. T
is called the transpose of A and is denoted by A or A A will be a matrix of order n m .
1 4
1 3 5
Example: If A then A 3 7
4 7 8
2 3 5 8
3 2
1 2 1 0
B
Example: If A , B , find A B A B , 2A 3 , 2A 3 , 5A B ,
,
B
3 4 4 7
A 7B
Solution:
1 2 1 0 1 1 2 0 0 2
A B
3 4 4 7 3 4 4 7 7 11

1 2 1 0 1 1 2 0 2 2
A B
3 4 4 7 3 4 4 7 1 3

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