Question 8. Reorder the columns of equations (2) by switching 2:5 with the variable which became 0 when moving from P to Q Apply row operations to put the resulting equations back into reduced row echelon form. Questions 1-8 exhibit the basic steps of the simpiea: method. We have some region we want to explore, given by linear equations ALE = 3, and by inequalities 3:1, :52, . . . , an 2 0. We start at some point P where 33.2.4.1 = mk+2 = -- - = an 2 0; these are known as the basis variables. The matrix A is in row reduced form with pivot columns at the non-basis variables and free columns at the basis variables. We chose one variable to remove from the basis and use the method sketched in Question 7 to put another variable into the basis. Then we rearrange our equations to have their pivot columns in the new non-basis variables. We'll describe the computation in Questions 7-8 as saying that we started with basis variables {3:5, 3:5, 2:7, 373} and exchanged 2:5 for a new basis variable. What we have omitted so far is the discussion of why we would want to do this. Generally, we have an objective function: A quantity which we want to make smaller or larger. Let us suppose, for example, that we wanted to make :31 larger