Let
A=[210031005]A = \begin{bmatrix} 2 & 1 & 0 \\ 0 & 3 & 1 \\ 0 & 0 & 5 \end{bmatrix}A=200130015
and let λmax\lambda_{\max}λmax be the largest eigenvalue of AAA.
Which vector below is an eigenvector of AAA for λmax\lambda_{\max}λmax, scaled so that its first entry is 111?
Select all that apply.
(1, 13, 16)\left(1,\ \tfrac{1}{3},\ \tfrac{1}{6}\right)(1, 31, 61)
(1, 3, 2)(1,\ 3,\ 2)(1, 3, 2)
(1, −3, −6)(1,\ -3,\ -6)(1, −3, −6)
(1, 3, 6)(1,\ 3,\ 6)(1, 3, 6)