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