Marcy inherited $25,000 and invested part of it in a money market account (x), part in municipal bonds (y), and part in a mutual fund (z). After one year, she received a total of $1,620 in simple interest from the three investments. The money market paid 6% annually, the bonds paid 7% annually, and the mutual fund paid 8% annually. There was $6,000 more invested in the bonds than the mutual funds. The goal of this problem will be to find the amount that Marcy invested in each category. To do so, follow these steps. Write the system of equations that is needed to solve this problem. Use variables x, y, and z as defined above. Write this system in matrix form AX = B, where A is a 3x3 matrix, X is the matrix x y, and B is a 3 x 1 matrix 2 representing the right-hand side. If the terminology is a bit foggy, remember that you handled problems like this in section 2.5 (Matrix Inverses) X = Using technology, find A-. Write all your entries in fraction form if possible (your graphing calculator should do this, please let me know if your method doesn't allow you to do this). DO NOT DO THIS BY HAND. Recall that the solution to this system is X = A-B. Compute this report how much should be invested in each account. Solve this same problem, but change the total invested to $40,000, the total interest to $2300, and using $8,000 more invested in bonds than mutual funds (instead of $6,000). How much should be invested in each fund to meet these new goals?