Hello,

The answer to your question will be solved in the following manner:

Lets assume that the person invests "x" amount in the first part, then the remaining amount will be "50000- x" since the whole amount is 50000. Now we have investment amounts for both parts i.e. "x" for the first part and "50000- x" for the second part.

We know that the interest rates on the respective parts are 10% and 12%. So that will amount to 0.1 and 0.12 respectively.

The total amount of interest should result in 5600 so we have to form matrix in such a way that at the end of the year we get 5600 interest rate from 50000 invested.

The answer will be as follows: M

Matrix A = [x     50000- x]

Matrix B =    [0.1

0.12]

Solving the matrix we get

[x     50000-x ]  *  [0.1        =   5600

0.12]

[x * 0.1+ (50000-x)*0.12] = 5600

0.1x + 6000- 0.12x = 5600

0.02x = 400

x = 20000

Therefore the investment in first part will be20000 and investment in second part will be 50000-20000=30000.

Final answer will be 20000 and 30000 .

Hope it helps!