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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 \[H=[h_{jk}]\] 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

\[Img(h_{jk})=B\]

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.

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

Note by Milun Moghe
3 years, 11 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 - 3 years, 11 months ago

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

Milun Moghe - 3 years, 11 months ago

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