Page 114 - DMTH201_Basic Mathematics-1

Unit 4: Determinants

The total cost of the two Production Departments, denoted by P and P , is given by Notes
1 2
39994.19
P 60000 0.40 0.35 0.25 106493.24
1 29995.64
P = 74000 0.20 0.40 0.20 109994.77
2 79988.37
Thus, P = 1,06,493.24 and P = 1,09,994.77.
1 2

Example

An amount of 4,000 is distributed into three investments at the rate of 7%, 8% and 9% per
annum respectively. The total annual income is 317.50 and the annual income from the first
investment is 5 more than the income from the second. Find the amount of each investment.
Solution:
Let x , x and x denote the amount of first, second and third investments respectively. We can
1 2 3
write
x + x + x = 4,000 .... (1)
1 2 3
Also 0.07x + 0.08x + 0.09x = 317.50
1 2 3
or 7x + 8x + 9x = 31,750 .... (2)
1 2 3
Further, 0.07x – 0.08x = 5
1 2
or 7x – 8x = 500 .... (3)
1 2
Writing the above equations in matrix form

1 1 1 x 1 4000
7 8 9 x = 31750 or AX = D
2
7 8 0 x 500
3
Here |A| = 23
4000 1 1
Also |A | = 31750 8 9 = 34500,
1
500 8 0

1 4000 1
|A | = 7 31750 9 = 28750
2
7 500 0
1 1 4000
and |A | = 7 8 31750 = 28750
3
7 8 500

34500
x = = 1,500
1
23
28750
and x = x 3 = 1,250.
2
23

LOVELY PROFESSIONAL UNIVERSITY 107