Hello Dr. Tsumura,

I would like to ask whether the third eigenvector is [2; -1; 0] or [1; -1; 1]?

Hope to hear back from you soon. Thank you.

Regards,

Anthony.

I am not sure what you mean by “the third eigenvector” but neither

\[\begin{bmatrix}

2 \\

-1 \\

0

\end{bmatrix} \text{ nor } \begin{bmatrix}

1 \\

-1 \\

1

\end{bmatrix}\]
is an eigenvector of the matrix $A$.

Hint: consider the difference of the second and the third equalities.

Thank you, Dr. Tsumura for replying and the hint.