The discussion revolves around finding the vertices of a polyhedron defined by a set of linear equations and constraints using the simplex method. Participants explore the implications of these equations, the setup of the simplex tableau, and the conditions for linear independence among the columns of the associated matrix.
Participants do not reach a consensus on the correctness of the initial solutions or the structure of the matrix. There are multiple competing views regarding the setup of the simplex tableau and the implications of linear independence.
There are unresolved issues regarding the constraints on the transformed variables and the correct formulation of the matrix. The discussion also reflects varying interpretations of the linear independence of the columns and the implications for the simplex method.
I like Serena said:Normally a polyhedron consists of a number of vertices connected by edges, such that faces (polygons) are formed.
A polyhedron usually has a certain volume.
If there are 2 faces or less, it won't contain a volume, and is considered degenerate.
In this case we don't even have a face - only a single line segment. (Nerd)
evinda said:So in this case we can say that if the line segment is one of the edges of a polyhedron , then its endpoints are vertices of the polyhedron. Right? (Thinking)
I like Serena said:Exactly. (Nod)