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Math Help - Need help with NxN matrix!

  1. #1
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    Need help with NxN matrix!

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

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  2. #2
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    Tejas
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    Re: Need help with NxN matrix!

    subtract the first row from every other row (this won't change the determinant). this gets you:

    \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:

    \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.
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