An amount of Rs. 10,000 is put into three investments at the rate of 10,12 and 15 per cent per annum. The combined income is Rs. 1,310 and the combined income of the first and the second investment is Rs. 190 short of the income from the third.
i) Represent the above situation by matrix equation and form the linear equation using multiplication.
ii) Is it possible to solve the system of equations so obtained using matrices?
let x, y and z be the three investment at the rate of 10 , 12 and 15 % per annum respectively.
the income on sum Rs. x is .
the combined income is
the equation can be re-written as:
since the combined income of 1st and 2nd is Rs.190 less than the income on 3rd sum.
the equation (1), (2) and (3) can be written in the form of AX=B
now to check whether the solution is consistent, we will find determinant of A.
i.e. (by using )
since det A is not equal to zero, therefore solution exist. we will solve this system of equation by Cramer's rule.
by using 
thus the investment at 10, 12 and 15 % per annum are 2000/- , 3000/- and 5000/- respectively.
hope this helps you.