Let , and let be the set of all matrices whose entries are all chosen from the set . Then the sum of the determinants of all these matrices
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0 marksMathematicsMatrices, determinants and linear systemsDeterminants and their propertiesVery Hardabout 4 min
DSE 2016 Question 19: Matrices, determinants and linear systems
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Let n>1, and let S be the set of all n× n matrices whose entries are all chosen from the set {0,1}. Then the sum of the determinants of all these matrices (A) is equal to 0 (B) is positive but less than n^(n/2) (C) can be positive or negative, but is bounded by nⁿ (D) is either -1 or 1
Also written as: Let n>1, and let S be the set of all n* n matrices whose entries are all chosen from the set {0,1}. Then the sum of the determinants of all these matrices
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What this question tests
This question is on Determinants and their properties, part of Matrices, determinants and linear systems in Mathematics.
Computing determinants and how row and column operations change them.
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