Use the indicated row operation to change each matrix. Then explain why that row operation should be applied to the matrix. 1. Replace R by R + (-4) R 14 7 4 1 2 3 10 6 lo 45 11 2. Replace R by R + (-3)R [1 6 4 022 S 10 5 3 171 3. Replace Ry by R [1 0 0 130 010 17 lo o 8 160 4. Use the Gauss-Jordan method to solve this system of equations. Show the row operations used at each step. Do not use your calculator. 4x - 2y = 3 -2x + 3y = 1 Use the Gauss-Jordan method to solve these systems of equations. You may use your calculator. Write out the matrix you input and the output matrix. Write out the solution, if one exists. If not, explain why. 5. 3x-4y-z = 1 2x-3y+z=1 x-2y+3z=2 6. 5x-3y + 2z=13 2x-y-3z=1 4x-2y + 4z = 12 Construct a system of linear equations for each of the following problems. Use Gauss-Jordan elimination to solve the system and then express the solution in terms of the problem. 7. A chemical manufacturer wants to lease a fleet of 24 railroad tank cars with a combined carrying capacity of 520,000 gallons. Tank cars with three different carrying capacities are available: 8,000 gallons, 16,000 gallons, and 24,000 gallons. How many of each type of tank car should be leased?