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I have a homework assignment which is: You have a matrix which is regular ($ A * A' = I$ ), and the sum of each row = $C$. Prove that the sum of each row in $A'$ are equal ( $= D$ ). And then find the relation between $C$ and $D$.

I am having trouble with this question - could someone please help me out? Thanks

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What does $A'$ mean? Is that the transpose of $A$? – Gerry Myerson Nov 28 '11 at 11:14
The Inverse of $A$ – Jhon Nov 28 '11 at 11:25
up vote 1 down vote accepted

Let $v$ be the all-ones vector. Then $Av$ is the all-$C$ vector, and $A'Av=Iv=v$. But also $A'Av=A'(Av)$. So $A'(Av)=v$, and $Av$ is the all-$C$ vector; what does that tell you about the row sums in $A'$?

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Great :) Thanks alot – Jhon Nov 28 '11 at 11:41

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