Linear Algebra and Its Applications · Problem 8.3.5

Linear Programming and Game Theory — Gilbert Strang

Mathematics · linear-programming-duality-both-empty

Problem

Starting with the 2 by 2 matrix

A = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}

, choose

b

and

c

so that both of the feasible sets

Ax \geq b

x \geq 0

and

yA \leq c

y \geq 0

are empty.