# calculate matrices

• Jan 14th 2013, 05:08 AM
wattskickin
calculate 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 AM
emakarov
Re: 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 AM
kalyanram
Re: calculate matrices
Quote:

Originally Posted by wattskickin
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?

I hope this is what you mean.
How many 6x6 matrices $A$ can be there such that $A = A^T$. Elements of the matrices can be selected from the set $\{0,1\}$?

Sol: For $A=A^T$ we need $a_{ij} = a_{ji}$ where $a_{ij}$ is the element in the $i^{th}$ row $j^{th}$ column.
We consider the elements $a_{ij}$ where $i \le j$(why ?). There are 21 such elements and for each of these elements we have 2 choices so we have $2^{21}$ such matrices.

Kalyan.