## Return to Answer

2 defer

Edit: I wanted the following matrix to be $W$. Robert Israel suggested I call it $W^T$ instead. I defer to his years of experience and the fact that it gives a better answer to the problem. End Edit.

For 6 times the given matrix, I nominate the following candidate for $W$W^T$$$\begin{bmatrix} 1 & & & & 1 & & & & 1 \\ 1 & & & & & 1 & & 1 & \\ & 1 & & 1 & & & & & 1 \\ & 1 & & & & 1 & 1 & & \\ & & 1 & 1 & & & & 1 & \\ & & 1 & & 1 & & 1 & & \end{bmatrix}$$ Does this help? Gerhard "Ask Me About Binary Matrices" Paseman, 2011.07.28 1 For 6 times the given matrix, I nominate the following candidate for$W\$

$$\begin{bmatrix} 1 & & & & 1 & & & & 1 \\ 1 & & & & & 1 & & 1 & \\ & 1 & & 1 & & & & & 1 \\ & 1 & & & & 1 & 1 & & \\ & & 1 & 1 & & & & 1 & \\ & & 1 & & 1 & & 1 & & \end{bmatrix}$$

Does this help?

Gerhard "Ask Me About Binary Matrices" Paseman, 2011.07.28