Answer
This transformation maps every vector to its orthogonal projection in the $xz$ plane.
Work Step by Step
Let $A$ be a $m\times n$ matrix corresponding to the linear transformation, say $T$. Then $T$ is defined by $T(v)=Av$, for all $v$ in the given domain.
Given $A = \left[ {\begin{array}{*{20}{c}}
1&0&0\\
0&0&0\\
0&0&1
\end{array}} \right]$
Then
$T\left( {\left[ {\begin{array}{*{20}{c}}
x\\
y\\
z
\end{array}} \right]} \right) = \left[ {\begin{array}{*{20}{c}}
1&0&0\\
0&0&0\\
0&0&1
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
x\\
y\\
z
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
x\\
0\\
z
\end{array}} \right]$
Hence, this transformation maps every vector to its orthogonal projection in the $xz$ plane.
