# Tagged Questions

1answer
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### condition for having a positive solution to a linear equation.

Let $Y$ be a member of $\mathbb{R}^m$. I need a necessary and sufficient condition on a $n\times m$ binary matrix $A$ for having a solution to the linear equation: $$AX=Y$$ Such that $X_i\geq 0$, ...
0answers
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### Area of a 2D convex polytope made of halfspaces

For a computer program I am attempting to solve the area of a convex polytope defined by a finite number of halfspaces. I understand that this forms a polygon and given the vertices of a polygon I am ...
2answers
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### Very symmetric convex polytope

Let $C_n$ be the convex polytope in ${\mathbb R}^n$ defined by the inequalities (in $n$ variables $x_1,x_2, \ldots ,x_n$) : $$x_i \geq 0, x_i+x_j \leq 1$$ (for any indices $i<j$). Denote by ...
1answer
305 views

### Polytopes and matrices

How can one show that the vertices of a polytope are the matrices contains 2 ones on each row and col? and if $M \in P$ is not a $Z_2$ matrix then $M$ is a derived ...
1answer
186 views