## Are These Linear Transformations?

## Problem 717

Define two functions $T:\R^{2}\to\R^{2}$ and $S:\R^{2}\to\R^{2}$ by

\[

T\left(

\begin{bmatrix}

x \\ y

\end{bmatrix}

\right)

=

\begin{bmatrix}

2x+y \\ 0

\end{bmatrix}

,\;

S\left(

\begin{bmatrix}

x \\ y

\end{bmatrix}

\right)

=

\begin{bmatrix}

x+y \\ xy

\end{bmatrix}

.

\]
Determine whether $T$, $S$, and the composite $S\circ T$ are linear transformations.