Orthogonal projection onto a plane (2)

#linear_algebra

Let $a, b \in R$ and $T : R^{3} \to R^{3}$ be the linear transformation that is orthogonal projection onto the plane $z = a x + b y$ (with respect to the usual Euclidean inner-product on $R^{3}$ ).
(a) Find the eigenvalues of $T$ and bases for the corresponding eigenspaces.
(b) Is $T$ diagonalizable? Justify.
(c) What is the characteristic polynomial of $T$ ?

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Let $a, b \in {\bf R}$ and $T: {\bf R}^3 \to {\bf R}^3$ be the linear transformation that is orthogonal projection onto the plane $z=ax+by$ (with respect to the usual Euclidean inner-product on ${\bf R}^3$).
\begin{enumerate}[label=(\alph*)]
	\item Find the eigenvalues of $T$ and bases for the corresponding eigenspaces.
	\item Is $T$ diagonalizable? Justify.
	\item What is the characteristic polynomial of $T$?
\end{enumerate}