Write the system of equations. Express it in Matrix form AX=b. Indicate what is A, what is X and what is b. Using Excel to find the inverse of A you obtained in 1. Solve the system using Excel. Randomly write another 3x3 matrix B. Find A+B, 2A, A*B, AT using Excel.

A bank wishes to invest a $100,000 trust fund in three sources: a bond fund paying (Pick one: 6%, 7%, 8%); a health sciences fund paying (Pick one: 8%, 9%, 10%); and a real estate fund paying (10%, 11%, 12%). The bank wishes to realize an $9000 annual income from the investment. A condition of the trust is that the total amount invested in the bond fund and the health sciences fund must be triple the amount invested in the real estate fund. How much should the bank invest in each possible category? Let x, y, and z, respectively, be the amounts invested in the bond fund, the health science fund, and the real estate fund. Set up the system of equations in x, y, z.