MathDB
ISI 2018 #8

Source: ISI B.Stat / B.Math Entrance Exam 2018

May 13, 2018
isiIndian Statistical Institute2018college contestslinear algebra

Problem Statement

Let n⩾3n\geqslant 3. Let A=((aij))1⩽i,j⩽nA=((a_{ij}))_{1\leqslant i,j\leqslant n} be an n×nn\times n matrix such that aij∈{−1,1}a_{ij}\in\{-1,1\} for all 1⩽i,j⩽n1\leqslant i,j\leqslant n. Suppose that ak1=1  for all 1⩽k⩽na_{k1}=1~~\text{for all}~1\leqslant k\leqslant n and   ∑k=1nakiakj=0  for all i≠j~~\sum_{k=1}^n a_{ki}a_{kj}=0~~\text{for all}~i\neq j.
Show that nn is a multiple of 44.
Back to ProblemsView on AoPS