# Thread: calculate matrices

1. ## calculate matrices

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

How many 6 x 6 (0, 1)-matrices A are there with A = A^tr?

2. ## Re: calculate matrices

Maybe you can find first how many symmetric 2 x 2 and 3 x 3 (0, 1)-matrices there are.

3. ## Re: calculate matrices

Originally Posted by wattskickin
Please help, I searched the text several times but could not figure out how to solve this problem

How many 6 x 6 (0, 1)-matrices A are there with A =A^tr?
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.