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1. Consider the two-loop circuit shown in gure 1. The currents I1 and I2 (in Amps) satisfy the following system of equations: 16I1 − 9I2 = 110 20I2 − 9I1 + 110 = 0 a. Setup: Describe the setup of this problem (e.g. include a diagram of problem, a list of what is known/given and a list of that is being found). b. Calculation: Write the system of equations in matrix form AI = b where I =  I1 I2  Find I1 and I2 using the matrix algebra method. Perform all computations by hand and show all steps. c. Calculation: Find I1 and I2 using Cramer's Rule. Perform all computations by hand and show all steps.2. A two-bar truss supports a weight of W = 750lb as shown in gure 2. Figure 1: Circuit diagram of a two loop circuit described in problem 1 The Forces F1 and F2 satisfy the following system of equations: 0.866F1 = F2 0.5F1 = 750 a. Setup: Describe the setup of this problem (e.g. include a diagram, a list of what is known/given and list of what is being found). b. Calculation: Write the system of equations in matrix form AF = b where F =  F1 F2  Find F1 and F2 using the matrix algebra method. (N.B. for this problem some coecients and/or constants will be zero). Perform all computations by hand and show all steps. c. Calculation: Find F1 and F2 using Cramer's Rule. Perform all computations by hand and show all steps. Figure 2: Diagram of the two-bar truss described in problem 2 13. You have two sugar solutions. One is 1.2 L with concentration of 1.5 g/L. The other is 0.6 L with concentration of 1.0 g/L. These two solution are mixed together thoroughly. a. Setup: Describe the setup of this problem (e.g., include a diagram of problem, a list of what is known/given and a list of what is being found) b. Calculation: What is the nal volume and concentration of sugar in g/L of the mixture? 4. For Halloween an M and M Mars Plant wants to make up a 150 bar mixture of 3-Musketeers and Snickers bars that is 40% 3 Musketeers bars. They have stock pallets that have 70% 3-Musketeers bars and 20% 3-Musketeers bars. How many bars should they take from each stock to make the correct mixture? a. Setup: Describe the setup of this problem (e.g., include a diagram of problem, a list of what is known/given and a list of what is being found). b. Calculation: Write the total material balance and the bar component balance equations for this problem. c. Calculation: Write the system of equation in matrix form AX = b, where X has the variable for number of bars from the 70% mixture in its rst row and the variable for total number of bars from the 20% mixture in its second row. Solve using matrix algebra method. Perform all computations by hand and show all steps. 5. A stream from a well water system is owing at 1.2 liters/min. The water in this stream has a chlorine concentration of 0.2 mg/liter. To treat this water we wish to bring the concentration up to 0.5 mg/L. You can mix in a solution of chlorine that has 50 mg/L of chlorine. How much of this solution do you need to add per hour? What is the resulting total ow rate as a result of this addition? a. Setup: Describe the setup of this problem (e.g., include a diagram of problem, a list of what is known/given and a list of what is being found). b. Calculation: Write the total material balance and the chlorine component balance equations for this problem. c. Calculation: Write the system of equation in matrix form AX = b, where X has the variable for the resulting total ow rate in its rst row and the variable for the total ow rate in its second row. Solve using Cramer's rule. Perform all computations by hand and show all steps.

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