## Is the Following Function $T:\R^2 \to \R^3$ a Linear Transformation?

## Problem 627

Determine whether the function $T:\R^2 \to \R^3$ defined by

\[T\left(\, \begin{bmatrix}

x \\

y

\end{bmatrix} \,\right)

=

\begin{bmatrix}

x_+y \\

x+1 \\

3y

\end{bmatrix}\]
is a linear transformation.