Investment Calculation Using Matrix Method
How can we calculate the amount of each investment using the matrix method?
An amount of Rs 5000 is put into three investments of 6%, 7%, and 8% per annum respectively. The total amount income from these investments is Rs 358. If the total annual income from the first two investments is Rs 70 more than the income of the third, find the amount of each investment by the matrix method.
Solution:
The question involves solving a system of linear equations to find three unknown investments using matrix methods. The student is provided with the combined invested amount, total annual income, and the relationship between incomes from these investments. By setting up a system of equations, the amounts invested at different interest rates can be determined.
Explanation: The question involves the calculation of investments and returns, which falls under the subject of Mathematics. Specifically, it relates to linear algebra, where a matrix method can be used to solve a system of equations. The student is in High School, as this level of math is typically introduced in this grade. To solve this problem, we must set up a system of equations based on the given information.
We have three unknown investments, let's denote them as x, y, and z, representing the investments at 6%, 7%, and 8% respectively. The total amount invested is Rs 5000, so the first equation would be:
x + y + z = 5000
The total annual income from these three investments is Rs 358, which gives us our second equation:
0.06x + 0.07y + 0.08z = 358
The third equation is based on the fact that the total annual income from the first two investments is Rs 70 more than the income from the third investment. This translates to:
0.06x + 0.07y = 0.08z + 70
With these three linear equations, we can create a matrix and use various matrix operation techniques to find the values of x, y, and z that satisfy all equations. Solving this system will yield the amounts of each investment.