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\begin{document}

\thispagestyle{empty}
\centerline{\sc Problem Set Eight: Due Friday, December 4}

\begin{Problem}
Let $M$ be a $k \times n$ matrix of rank $k$ all of whose $k \times k$ minors are nonnegative.
Let $P$ be the leftward pivot column positions of $M$; assume that $1 \in P$ and $n \not\in P$. 
Put $P = S \sqcup \{ 1 \}$. Let $T$ be any $(k-1)$-element subset of $\{ 2,3,\ldots,n-1 \}$ such that $\Delta^{T \cup \{ 1 \}}(M) \neq 0$. Show that
\[  \Delta^{S \cup \{ n \}}(M) \Delta^{T \cup \{ 1 \}}(M) \geq  \Delta^{S \cup \{ 1 \}}(M) \Delta^{T \cup \{ n \}}(M) . \]
\end{Problem}


\end{document}


