An amount of ₹10,000 is put into three investments at the rate of 10, 12 and 15% per annum. The combined incomes are ₹1310 and the combined income of first and second investment is ₹ 190 short of the income from the third. Find the investment in each using matrix method.

Question

Philoid · Accepted Answer

Let the numbers are x, y,z

x + y + z = 10,000 ……(i)

Also,

0.1x + 0.12y + 0.15z = 1310 …… (ii)

Again,

0.1x + 0.12y – 0.15z = – 190 …… (iii)

A X = B

|A| = 1(– 0.036) – 1(– 0.03) + 1(0)

= – 0.006

Hence, the unique solution given by x = A ^{– 1}B

C_{11 =} – 0.036

C₁₂ = 0.27

C₁₃ = 0

C₂₁ = 0.27

C₂₂ = – 0.25

C₂₃ = – 0.02

C₃₁ = 0.03

C₃₂ = – 0.05

C₃₃ = 0.02

X = A ^{– 1} B =

Adj A =

X =

=

Hence, x = Rs 2000, y = Rs 3000 and z = Rs 5000