I'm not really sure how to prove this is a linear transformation. I couldn't find a definition for a linear transformation either which made the problem more confusing.Let $\displaystyle T : \Re \rightarrow \Re ^3$ be given by $\displaystyle T \begin{pmatrix}

{x}\\

{y}\\

{z}

\end{pmatrix}=\begin{pmatrix}

{x}\\

{y}\\

{0}

\end{pmatrix}$. This is projection from 3-space onto the xy-plane. Show that T is a linear transformation. What is the matrix associated to T?

I also don't know what it means by "matrix associated to T". Is this all it wants:

$\displaystyle \begin{pmatrix}

{1}&{0}&{0}\\

{0}&{1}&{0}\\

{0}&{0}&{0}

\end{pmatrix}\begin{pmatrix}

{x}\\

{y}\\

{z}

\end{pmatrix}=\begin{pmatrix}

{x}\\

{y}\\

{0}

\end{pmatrix}$

?

Help would be appreciated!