Questions askedCategory: 2568MATH 2568 Practice Problem Question 9

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.

Yu Staff answered 10 months ago

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.