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???????

#Algebra #Matrices

Easy Math Editor

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Comments

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

Milun Moghe - 7 years, 3 months ago

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, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$