# 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 \$\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.