QCEVault

Matrices and applications — Question 197

Original QCE Vault practice · 5 marks

Q197 · Practice questionTechnology-activeComplex familiar5 marks

QUESTION 197 (5 marks)

In a tournament A beats B, B beats C and C beats A. Define Dij=1D_{ij}=1 if i beats j and 0 otherwise, in order A,B,C. There are no draws.
Three tournament nodes A, B and C with arrows A to B, B to C and C to A. Each arrow means its source beats its destination.
a)
Write D and its square.
[2 marks]
b)
Compute its cube and interpret its diagonal. Are these self-victories?
[3 marks]
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