Y by anantmudgal09, Wizard_32, Adventure10, TFIRSTMGMEDALIST, Mango247, Deadline
Let
and
be real numbers. Let
be the matrix with entries
Suppose that
is an
matrix with entries
,
such that the sum of the elements in each row and each column of
is equal to the corresponding sum for the matrix
. Prove that
.



![\[a_{ij} = \begin{cases}1,&\text{if }x_i + y_j\geq 0;\\0,&\text{if }x_i + y_j < 0.\end{cases}\]](http://latex.artofproblemsolving.com/c/0/8/c0856fe7b2b113180659952c4d216a01d8849f64.png)







This post has been edited 4 times. Last edited by MellowMelon, Nov 13, 2018, 7:56 PM
Reason: fix typo: x_n -> y_n
Reason: fix typo: x_n -> y_n