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1. The reduced row echelon form of the augmented matrix of a system of equations is given. Find the solutions of the system. 2 664 1 0 0 2 15 0 1 0 1 􀀀7 0 0 1 0 􀀀8 0 0 0 0 0 3 775 2. Use row operations to solve the system x + y 􀀀 z = 􀀀5 3x 􀀀 y + z = 1 x 􀀀 4y + 2z = 􀀀19 3. Use row operations to solve the following system of equations 􀀀21x 􀀀 2y + z = 􀀀13 12x + y = 9 􀀀24x 􀀀 2y + z = 􀀀16 4. An investment of $103,000 was made by a business club. The investment was split into three parts and lasted for one year. The rst part of the investment earned 8% interest, the second 6% and the third 9%. Total interest from the investments was $8070. The interest from the rst investment was 6 times the interest from the second. Find the amounts of the three parts of the investment. What is the amount of the rst part of the investment? 5. The controller (money manager) for a small company puts some money in a bank account paying 5% per year. He uses some additional money, amounting to 1 3 the amount placed in the bank, to buy bonds paying 6% per year. With the balance of the funds, he buys a 10% certicate of deposit. The rst year the investments bring a return $791. If the total of this investments is $10,000 how much is invested at each rate? 1

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