# 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.

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 – 1B

C11 = – 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 =

X =

X =

=

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

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