Consider the matrix $\left[\begin{array}{ll}1 & k \\ 2 & 1\end{array}\right]$, where $k$ is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix?
- $\left[\begin{array}{c}1 \\ -\sqrt{2 / k}\end{array}\right]$
- $\left[\begin{array}{c}1 \\ \sqrt{2 / k}\end{array}\right]$
- $\left[\begin{array}{c}\sqrt{2 k} \\ 1\end{array}\right]$
- $\left[\begin{array}{c}\sqrt{2 k} \\ -1\end{array}\right]$