Mathematics Asked by user4164 on December 15, 2020

Consider a matrix

$$

A=

begin{pmatrix}

a_{11} & a_{12} & a_{13} & a_{14} & a_{15} & a_{16} \

a_{21} & a_{22} & a_{23} & a_{24} & a_{25} & a_{26}

end{pmatrix},

$$

in which sum of the elements of each colon is zero and $a_{i,j}=pm1$.

Suppose also that $E(A)=C$.

Define sub-matrices $A_1=begin{pmatrix}

a_{11} & a_{12}\

a_{21} & a_{22}

end{pmatrix}$,

$A_2=begin{pmatrix}

& a_{13} & a_{14}\

& a_{23} & a_{24}

end{pmatrix}$, $A_3=begin{pmatrix}

& a_{15} & a_{16} \

& a_{25} & a_{26}

end{pmatrix}$.

Is it possible to represent expectations of $A_1, A_2, A_3$ through $E(A)=C$?

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