QCEVault

Further matrices — Question 276

Original QCE Vault practice · 6 marks

Q276 · Practice questionTechnology-freeComplex familiar6 marks

QUESTION 276 (6 marks)

Three teams A, B and C play a mini-tournament. A defeats B, B defeats C, and C defeats A. Let Dij=1D_{ij}=1 when team i defeats team j and 0 otherwise, with order A, B, C.
a)
Construct D and determine the row-sum scores of D+D2D+D^2.
[2 marks]
b)
An organiser says changing the model to D+qD2D+qD^2 for positive q will produce a unique ranking. Evaluate the claim.
[2 marks]
c)
Propose one refinement that could distinguish the teams. State any additional information it would require.
[2 marks]
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