Learning Objectives: For the Session 05 Pre-lab Exercise you must successfully master the following tasks in Excel: 1. Solve for a single variable using Goal Seek. 2. Solve for a system of linear equations using Matrix Algebra, Cramer's Rule, and Solver. 3. Solve for a system of non-linear equations using Solver. For this exercise, you will be given several tasks that ask you to solve for either a single variable or multiple variables. Review your lab manual before starting the pre-lab exercise. - Important - Before you begin: 1. Make sure that iterative calculations are turned on. 2. Make sure that the maximum change value is 1.0x10-15. 3. Make sure that you have the Solver add-in. Please see your lab manual for the steps needed to check the Solver add-in, turn on the iterative calculations, and to make sure that the maximum change value is set to 1.0x10-15. The pre-lab exercise and the exercise during class cannot be completed if you do not have these three things! Given the following set of linear equations: 3.2 x + 5y +7 z = 8.4 3 – 0.5 y + 6 z= 4.6 5 2 + y - 2 2= -0.7 [Equation 2.1] [Equation 2.2] [Equation 2.3] For this task, you will solve for x, y, and z using both Matrix Algebra and Cramer's Rule and answer the following questions. Question 3 What are the inverse coefficients of Equation 2.3? Give your answer to four decimal places. Inverse Coefficients: 5 x 18 1 y -2 z Question 4 Fill in the following determinants that were used for solving the system of equations with Cramer's Rule. Give your answer to two decimal places. a) D = $ b) Dx = c) Dy = G d) Dz = 4 Question 5 What are the solved values of x, y, and z? Give your answer to four decimal places. a) x = b) y = c) z = Question 6 What is the difference between using Matrix Algebra vs. Cramer's Rule? Cramer's Rule is an iterative method, whereas Matrix Algebra is not. No difference since both methods give you the same results. With Cramer's Rule, you can solve for an entire system of linear equations or for a single variable, but with Matrix Algebra you can only solve for the entire system of linear equations. With Matrix Algebra, you can solve for an entire system of linear equations or for a single variable, but with Cramer's Rule you can only solve for the entire system of linear equations. Matrix Algebra is an iterative method, whereas Cramer's Rule is not.