This is a calculus problem.Please show all work. Gauss Jordan and Matrix Inversion.

A small software corporation borrowed $145,000 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 detem'line how much was borrowed at each rate if the annual interest was $15,000 and the amount borrowed at 10% was 2'12 times the amount borrowed at 9%. Solve the system using matrices. amount borrowed at 9% $ :1 amount borrowed at 10% $ :1 amount borrowed at 12% $ :1