GATE 2020 BM – Question 9

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

A 4×4 matrix M=[mᵢⱼ] has zero diagonal and mᵢⱼ=−mⱼᵢ. What minimum number of entries determines the full matrix?

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Correct answer: (B) 6

Explanation

The diagonal is already fixed at zero. Each entry above the diagonal fixes its reflected below-diagonal partner by skew symmetry. There are 4×3/2=6 distinct off-diagonal pairs, so six independent entries suffice. Thus B.

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