Find the index of maximum element in a matrix given sum of rows and columns

80 Views Asked by At

For a matrix $\begin{bmatrix}a & b & c\\d & e &f \\ g & h & i\end{bmatrix}$, given sum of each row and column , how to find the index of the maximum element in the matrix? In other words, how to find argmax of joint distribution given all marginals?