Page 115 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes
Example
To control a crop disease, it is necessary to use 8 units of chemical A, 14 units of chemical B and
13 units of chemical C. One barrel of spray P contains 1 unit of A, 2 units of B and 3 units of C. One
Barrel of spray Q contains 2 units of A, 3 units of B and 2 units of C. One barrel of spray R contains
1 unit of A, 2 units of B and 2 units of C. Find how many barrels of each spray be used to just meet
the requirement?
Solution:
Let x barrels of spray P, y barrels of spray Q and z barrels of Spray R be used to just meet the
requirement.
The above information can be written as the following matrix equation.
x + 2y + z = 8
2x + 3y + 2z = 14

3x + 2y + 2z = 13

1 2 1 8
Let A = 2 3 2 and B 14
3 2 2 13

|A| = 6 + 12 + 4 – 9 – 4 – 8 = 1

2 2 1
A = Adj A 2 1 0
–1
5 4 1

x 2 2 1 8 1
y = 2 1 0 14 2
z 5 4 1 13 3

i.e. x = 1, y = 2, z = 3 barrels of spray P, Q and R respectively.

Example
An amount of 65,000 is invested in three investments at the rate of 6%, 8% and 9% per annum,
respectively. The total annual income is 4,800. The income from the third investment is 600
more than the income from second investment. Using matrix algebra, determine the amount of
each investment.
Solution:
Let x, y and z be the amount invested in the three investments. Thus, we can write
x + y + z = 65000

0.06x + 0.08y + 0.09z = 4800 or 6x + 8y + 9z = 4,80,000
–0.08y + 0.09z = 600 or 8y – 9z = –60,000

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