MATH 340 Lecture Notes - Lecture 9: Block Matrix, Dot Product, Identity Matrix
Document Summary
Now we want to go back to thinking about things in terms of matrices, and see how we can rephrase what we"re doing in the simplex method in terms of them. Remember that a while back we said that if we have an lp in standard form, we can write it succinctly in terms of matrices: if x1, . Now, the rst step of the simplex method was to add in slack variables, xn+1, . , xn+m (so m of them, the same m as in the dimension of a, since that"s the number of constraints). We let ~xs be this vector of slack variables in rm; then our modi ed lp is: maximize ~c ~xd, subject to a~xd + ~xs = ~b and ~xd, ~xs 0. Okay, so now this has two vectors of variables ~xd, ~xs, which is kind of awkward.
