Can someone explain how to solve this step by step? I have to find determinant(A).

http://i41.tinypic.com/r7k4uw.jpg

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- Nov 10th 2011, 08:36 AMDoomwarNeed help with NxN matrix!
Can someone explain how to solve this step by step? I have to find determinant(A).

http://i41.tinypic.com/r7k4uw.jpg - Nov 10th 2011, 09:43 AMDevenoRe: Need help with NxN matrix!
subtract the first row from every other row (this won't change the determinant). this gets you:

$\displaystyle \begin{vmatrix}-8&u&\dots&u\\u+8&-8-u&\dots&0\\ \vdots&\vdots&\ddots&\vdots\\u+8&0&\dots&-8-u\end{vmatrix}$

next, add every column to the first (this also will not change the determinant) to get:

$\displaystyle \begin{vmatrix}-8-u + nu&u&\dots&u\\0&-8-u&\dots&0\\ \vdots&\vdots&\ddots&\vdots\\0&0&\dots&-8-u\end{vmatrix}$

this shouldn't be too hard to calculate.