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GATE ECE 2006 | Question-21

The eigenvalues and the corresponding eigen vectors of a $2 \times 2$ matrix are given by

$$\begin{array}{cc} \textbf{Eigenvalue}& \textbf{Eigenvector} \\ \lambda_1=8 & \text{v}_{1} = \left[ \begin{array} {} 1 \\ 1 \end{array} \right] \\ \lambda_2=4 & \text{v}_{2} = \left[ \begin{array} {c} 1 \\ – 1 \end{array} \right] \end{array}$$

The matrix is

  1. $\left[\begin{array}{ll}6 & 2 \\ 2 & 6\end{array}\right]$
  2. $\left[\begin{array}{ll}4 & 6 \\ 6 & 4\end{array}\right]$
  3. $\left[\begin{array}{ll}2 & 4 \\ 4 & 2\end{array}\right]$
  4. $\left[\begin{array}{ll}4 & 8 \\ 8 & 4\end{array}\right]$
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