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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 ??
asked in Linear Algebra by Active (1.6k points)   | 42 views
@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

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