Radial expansion from a fixed line

#linear_algebra

Let $T : R^{3} \to R^{3}$ be the linear transformation that expands radially by a factor of three around the line parameterized by $L (t) = [\begin{matrix} 2 \\ 2 \\ - 1 \end{matrix}] t$ , leaving the line itself fixed (viewed as a subspace).

Find an eigenbasis for $T$ and provide the matrix representation of $T$ with respect to that basis.
Provide the matrix representation of $T$ with respect to the standard basis.

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Let $T:{\bf R}^3\to {\bf R}^3$ be the linear transformation that expands radially by a factor of three around the line parameterized by $L(t)=\begin{bmatrix} 2 \\ 2 \\ -1\end{bmatrix} t$, leaving the line itself fixed (viewed as a subspace).

\medskip
\begin{enumerate}[label=(\alph*)]
	\item Find an eigenbasis for $T$ and provide the matrix representation of $T$ with respect to that basis.
	\item Provide the matrix representation of $T$ with respect to the standard basis.
\end{enumerate}