A matrix AAA has an eigenvector v=(11)v = \begin{pmatrix} 1 \\ 1 \end{pmatrix}v=(11) corresponding to λ=2\lambda = 2λ=2. What is A10vA^{10} vA10v?
210(11)2^{10} \begin{pmatrix} 1 \\ 1 \end{pmatrix}210(11)
102(11)10^2 \begin{pmatrix} 1 \\ 1 \end{pmatrix}102(11)
2(11)2 \begin{pmatrix} 1 \\ 1 \end{pmatrix}2(11)
10(11)10 \begin{pmatrix} 1 \\ 1 \end{pmatrix}10(11)