Chapter 11.2, Problem 1ED

Let $M=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$

(A) Show that if the row minima belong to the same column, at least one of them is a saddle value.

(B) Show that if the column maxima belong to the same row, at least one of them is a saddle value.

(C) Show that if $\left(a+d\right)-\left(b+c\right)=0$ then $M$ has a saddle value (that is, $M$ is strictly determined).

(D) Explain why part (C) implies that the denominator $D$ in Theorem $4$ will never be $0$