# Determinant of a symmetric matrix values in each column and row don't repeat

Could you help me count the determinant of this symmetric matrix?

$\begin{vmatrix} a&2b&3c&6d\\b&a&3d&3c\\c&2d&a&2b\\d&c&b&a\end{vmatrix}$

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You can always ask W|A for assistance. The determinant does not have a simple form, it seems. You might want to double check for typos. –  Sasha Jan 22 '13 at 5:59
Ok. Do you know by any chance what to do with this determinant in order for it to be 0? And one more question. Is there any honest way to count this determinant? Is Laplace "effective" here? –  Hagrid Jan 22 '13 at 6:05
If it is symmetric, then $b=c=d=0$, and so the determinant is $a^4$. –  copper.hat Jan 22 '13 at 7:09
What you have displayed is a determinant, not a matrix. –  John Bentin Jan 22 '13 at 8:46
Perhaps the OP is using the word "symmetric" in the normal English sense. With that interpretation, his matrix is symmetric about one of its diagonals. –  bubba Jan 22 '13 at 8:51