Find an eigenvector for eigenvalue λ=2\lambda = 2λ=2 of the matrix A=(2005)A = \begin{pmatrix} 2 & 0 \\ 0 & 5 \end{pmatrix}A=(2005).
v=(10)\mathbf{v} = \begin{pmatrix} 1 \\ 0 \end{pmatrix}v=(10)
v=(01)\mathbf{v} = \begin{pmatrix} 0 \\ 1 \end{pmatrix}v=(01)
v=(11)\mathbf{v} = \begin{pmatrix} 1 \\ 1 \end{pmatrix}v=(11)
v=(25)\mathbf{v} = \begin{pmatrix} 2 \\ 5 \end{pmatrix}v=(25)