Projection onto a plane

#linear_algebra #projection #diagonalization

Let $T : R^{3} \to R^{3}$ be the orthogonal projection onto the plane $z = x + y$ , with respect to the standard Euclidean inner product.

Write the matrix representation of $T$ with respect to the standard basis.
Is $T$ diagonalizable? Justify your answer.

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code

Let $T:{\bf R}^3\to {\bf R}^3$ be the orthogonal projection onto the plane $z=x+y$, with respect to the standard Euclidean inner product.
	\begin{enumerate}[label=\alph*)]
		\item Write the matrix representation of $T$ with respect to the standard basis.
		
		\item Is $T$ diagonalizable? Justify your answer.
	\end{enumerate}