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GATE BT 2022 | Question: 29

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A $2\times 2$ matrix $\textbf{P}$ has an eigen value $\lambda_{1}=2$  with eigenvector $x_{1}=\begin{pmatrix} 1 \\ 0  \end{pmatrix}$ and another eigenvalue $\lambda_{2}=5,$ with eigenvector $x_{2}=\begin{pmatrix} 1 \\ 1  \end{pmatrix}.$ The matrix $\textbf{P}$ is

  1. $\begin{pmatrix} 2 & 0 \\ 0 & 5  \end{pmatrix}$
  2. $\begin{pmatrix} 2 & 3 \\ 0 & 5  \end{pmatrix}$
  3. $\begin{pmatrix} 1 & 1 \\ 0 & 1  \end{pmatrix}$
  4. $\begin{pmatrix} 1 & 1 \\ 1 & 0  \end{pmatrix}$

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