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Source: MTRP 2019 Class 11-Short Answer Type Problems: Problem 2 :-

April 9, 2020
combinatorics

Problem Statement

How many n×nn\times n matrices AA, with all entries from the set {0,1,2}\{0, 1, 2\}, are there, such that for all i=1,2,⋯ ,ni=1,2,\cdots,n Aii>∑j=1j≠inAijA_{ii} > \displaystyle{\sum \limits_{j=1 j\neq i}^n} A_{ij} [Where AijA_{ij} is the (i,j)(i,j)th element of the matrix AA]
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