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GATE ECE 2024 | Question: 45

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​​​​​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?

  1. $\left[\begin{array}{c}1 \\ -\sqrt{2 / k}\end{array}\right]$
  2. $\left[\begin{array}{c}1 \\ \sqrt{2 / k}\end{array}\right]$
  3. $\left[\begin{array}{c}\sqrt{2 k} \\ 1\end{array}\right]$
  4. $\left[\begin{array}{c}\sqrt{2 k} \\ -1\end{array}\right]$

 

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