(4%). An $m \times n$ array $A$ of real numbers is a Monge array if for any rows $1 \le i < k \le m$ and any columns $1 \le j < \ell \le n$, we always have

$A[i,j] + A[k,\ell] \le A[i,\ell] + A[k,j]$

(1)

In other words, for the four entries at rows $i,k$ and columns $j,\ell$, the sum of the upper-left and lower-right elements is always at most the sum of the lower-left and upper-right elements. Consider the following two arrays

$M_1 = \begin{bmatrix} 10 & 17 & 13 & 28 & 23 \\ 17 & 22 & 16 & 29 & 23 \\ 24 & 28 & 22 & 34 & 24 \\ 11 & 13 & 6 & 17 & 7 \\ 45 & 44 & 32 & 37 & 23 \\ 36 & 33 & 19 & 21 & 6 \\ 75 & 66 & 51 & 53 & 34 \end{bmatrix} \quad \text{and} \quad M_2 = \begin{bmatrix} 37 & 23 & 22 & 32 \\ 21 & 6 & 7 & 10 \\ 53 & 34 & 30 & 31 \\ 32 & 13 & 9 & 6 \\ 43 & 21 & 15 & 8 \end{bmatrix}$

It can be verified that $M_1$ is a Monge array and $M_2$ is not. Which of the followings are true?