Projection onto a plane

#linear_algebra

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

View

L A T E X

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}