42 views
Consider a $3\times 3$ matrix with every element being equal to 1 , its only non-zero eigenvalue is ....?

\begin{bmatrix} 1 & 1 &1 \\ 1 &1 &1 \\ 1 &1 &1 \end{bmatrix}$now i solve in simple way ..directly$\left | A-\lambda I \right |$THEN I got correct ans 0,0,5 but i have doubt .. if i solve by some elementary operation and reduce to$\begin{bmatrix} 1 & 1 &1 \\ 0& 0 &0 \\ 0 & 0 &0 \end{bmatrix}\$

but i got different eigen values  why this happened ... i missed something ??
@sid 1221 ,

the eigen values of above given matrix are : 0,0,3

and you will solve from any method(by using simple method or by using the elementary operations) you always find that the eigen values are : 0,0,3
ok any reference ?
engg. mathematics 1 by HK DASS