# Math Help - finding eigen values for nXn matrices

1. ## finding eigen values for nXn matrices

i dont know ho to make a trangle of zeros below the diagonal
if i subtract the first column from the rest i get zeros below the diagonal.
but the first column remain intact.

what to do with it
?

2. ## Re: finding eigen values for nXn matrices

Using the trasformations (i) $F_i\to F_i-F_1$ for all $i=2,\ldots,n$ and (ii) $C_1\to C_1+C_2+\ldots+C_n$ :

$\det (A-\lambda I)=\begin{vmatrix} -\lambda & \;\;a & \ldots & \;\;a\\ \;\;a &-\lambda & \ldots & \;\;a \\ \vdots&&&\vdots \\\;\; a & \;\;a &\ldots & -\lambda\end{vmatrix}=\ldots=[(n-1)a-\lambda](-a-\lambda)^{n-1}$

thanks