Orthogonal projection onto a plane

#linear_algebra

Let $T : R^{4} \to R^{4}$ be orthogonal projection to the $2$ -dimensional plane $P$ spanned by the vectors $v = (2, 0, 1, 0)$ and $w = (- 1, 0, 2, 0)$ .

Find (with proof) all eigenvalues and eigenvectors, along with their geometric and algebraic multiplicities.
Find the matrix representing $T$ with respect to the standard basis. Is this matrix diagonalizable? Why or why not?

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Let $T:{\bf R}^4\to {\bf R}^4$ be orthogonal projection to the $2$-dimensional plane $P$ spanned by the vectors ${\bf v}=(2,0,1,0)$ and ${\bf w}=(-1,0,2,0)$.
\begin{enumerate}[label=\alph*)]
	\item Find (with proof) all eigenvalues and eigenvectors, along with their geometric and algebraic multiplicities.
	\item Find the matrix representing $T$ with respect to the standard basis. Is this matrix diagonalizable? Why or why not?
\end{enumerate}