3. Investing: A trust fund manager has $200,000 to invest in three different investment options: accounts A, B and C. The projected annual yield for each of these investments is 7% for option A, 8% for option B and 10% for option C. Suppose the goal for the manager is to earn an average of 9% total interest from all investments. Note that means earning $18,000 total interest. Let a = the amount invested in option A, b = the amount invested in B and c = the amount invested in option C. a) Write a matrix to represent the system of equations that describes these assumptions. b) Write the reduced row echelon form of the matrix. Use calculator or computer to find the reduced row echelon form of the matrix and write the result here. c) Write the general solution to the system of equations. Use the parameter t as the free variable. d) If $120,000 is invested in account C, what amounts should be invested in the other accounts to satisfy the goals as stated