Solving systems using matrices

Question

A small software corporation borrowed $470,000 to expand its software line. Some of the money was borrowed at 9%, some at 10%, and some at 12%. Use a system of equations to determine how much was borrowed at each rate if the annual interest was $46,800 and the amount borrowed at 10% was 2½ times the amount borrowed at 9%. Solve the system using matrices.

amount borrowed at 9%	$
amount borrowed at 10%	$
amount borrowed at 12%	$

Answer 1

You can set up the simultaneous equations and then the matrix (A) is the coefficients, (x y z)^T which will stand for the 9 10 and 12% amounts of money allocated you are solving for and the solution vector that will be the column vector b. You will solve the matrix Ax = b

1) sum of money in x, y, z: 1x + 1y + 1z = 470K

2) amount earned .09x + .1y + .12z = 46.8K

3) Rel'n of x and y 2.5x + (-1)y + 0z = 0

I leave you the matrix problem.