Approaching to Matrices in a different way.

Friends this is a problem i had posted two weeks ago maybe . Did anyone find a pragmatic solution. This question is from the AITS which fiitjee conducts unfortunately i don't have the hints and solutions.I only know the answer.Do participate in this discussion. and try to help me out.

A matrix H=[hjk]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(hjk)=ARe(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)

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

det(H)=Ddet(H)=D D=E\left| D\right|=E

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

The answer is D is a non negative multiple of four. but how???????

Note by Milun Moghe
7 years, 5 months ago

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1 vote

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I think every one should discuss and maybe we can find out a solution.

Milun Moghe - 7 years, 5 months ago

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From the answer I came to a conclusion of proving that H=PP'. Where P'. is the transpose conjugate of P but how can we prove this?

Milun Moghe - 7 years, 5 months ago

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