Please help, I searched the text several times but could not figure out how to solve this problem(Wondering)

How many 6 x 6(0,1)-matricesAare there withA =A^tr?

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- Jan 14th 2013, 05:08 AMwattskickincalculate matrices
Please help, I searched the text several times but could not figure out how to solve this problem(Wondering)

How many 6 x 6*(*0*,*1*)*-matrices*A*are there with*A =**A^*tr? - Jan 14th 2013, 05:37 AMemakarovRe: calculate matrices
Maybe you can find first how many symmetric 2 x 2 and 3 x 3 (0, 1)-matrices there are.

- Jan 14th 2013, 05:48 AMkalyanramRe: calculate matrices
I hope this is what you mean.

How many 6x6 matrices $\displaystyle A$ can be there such that $\displaystyle A = A^T$. Elements of the matrices can be selected from the set $\displaystyle \{0,1\}$?

Sol: For $\displaystyle A=A^T$ we need $\displaystyle a_{ij} = a_{ji}$ where $\displaystyle a_{ij}$ is the element in the $\displaystyle i^{th}$ row $\displaystyle j^{th}$ column.

We consider the elements $\displaystyle a_{ij}$ where $\displaystyle i \le j$(why ?). There are 21 such elements and for each of these elements we have 2 choices so we have $\displaystyle 2^{21}$ such matrices.

Kalyan.