A lottery winner got $350,000 that invested as follows: part of it in a money market account, part in municipal bonds, and part in a mutual fund. After one year, he recieved a total of $24,200 in simple intersest from the three investments. The money market paid 6% annually, the bonds paid 7% annually, and the mutually fund paid 8% annaully. There was $40,000 more invested in the mutual funds than in bonds. Find the amount this person invested in each category. To solve the problem follow the following step:
a) write the system of equations that describes this problem. Identify clearly unknowns.
b) Express the sysem of equation in matrix form.
c) write a matlab script that will calculate :
i) the determinant of the system, and if the determinant is different from zero,
ii) find the inverse of the system matrix
iii) using the inverse,solve for the unknowns