An amount of ₹ 5000 is put into three investments at 6%, 7% and 8% per annum respectively. The total annual income from these investments is ₹358. If the total annual income from first two investments is ₹70more
than the income from the third, find the amount of each investment by the matrix method.
HINT: Let these investments be ₹x, ₹y and ₹z, respectively.
Then, x + y + z = 5000, …(i)
= 358
6x + 7y + 8z = 35800 …(ii)
And,
6x + 7y - 8z = 7000. …(iii)
Let these investments be ₹x, ₹y and ₹z, respectively.
Then, x + y + z = 5000
= 358
6x + 7y + 8z = 35800
And,
6x + 7y - 8z = 7000.
Representing in the matrix form,
AX = B
R3 – R2
R2 – 6R1
Converting back into the equations we get
X + y + z = 5000
Y + 2z = 5800
- 16z = - 28800
Z = 1800
Y + 2×1800 = 5800
Y = 5800 - 3600
Y = 2200
x + 2200 + 1800 = 5000
X = 5000 – 4000
X = 1000
Amount of 1000 , 2200 , 1800 were invested in the investments of 6% , 7%, 8% respectively.