Matrix or Football?

Algebra Level 4

A matrix \[H=[h_{jk}]\] is used to keep track of three football players (numbered 1,2 and 3) in three matches (1st,2nd and 3rd).

\[Re(h_{jk})=A\] A= number of matches in which both jth and kth players played or both did not play.

If j=k,A=3


B = (number of matcher played by kth player) - (number of matches played by jth player)

Let\[P=[P_{jk}]\] \[P_{jk}=C\] C=1 if jth player played in kth match and C=i otherwise \[i=(-1)^{0.5}\]

\[det(H)=D\] \[\left| D\right|=E\]

Only in the answer two parallel lines represent det and not absolute value.


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